Denoisingof3DBrainMRImageswithParallelResidual ...Parallel-RicianNet, which will combine global and...

Research ArticleDenoising of 3D Brain MR Images with Parallel ResidualLearningofConvolutionalNeuralNetworkUsingGlobal andLocalFeature Extraction

Liang Wu 1 Shunbo Hu 2 and Changchun Liu 1

1School of Control Science and Engineering Shandong University Jinan 250061 China2School of Information Science and Engineering Linyi University Linyi 276005 China

Correspondence should be addressed to Shunbo Hu 84961103qqcom and Changchun Liu changchunliusdueducn

Received 23 January 2021 Revised 15 April 2021 Accepted 21 April 2021 Published 4 May 2021

Academic Editor Vahid Rakhshan

Copyright copy 2021 Liang Wu et al is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Magnetic resonance (MR) images often suffer from random noise pollution during image acquisition and transmission whichimpairs disease diagnosis by doctors or automated systems In recent years many noise removal algorithms with impressiveperformances have been proposed In this work inspired by the idea of deep learning we propose a denoising method named 3D-Parallel-RicianNet which will combine global and local information to remove noise in MR images Specifically we introduce apowerful dilated convolution residual (DCR) module to expand the receptive field of the network and to avoid the loss of globalfeatures en to extract more local information and reduce the computational complexity we design the depthwise separableconvolution residual (DSCR) module to learn the channel and position information in the image which not only reducesparameters dramatically but also improves the local denoising performance In addition a parallel network is constructed byfusing the features extracted from each DCR module and DSCR module to improve the efficiency and reduce the complexity fortraining a denoising model Finally a reconstruction (REC) module aims to construct the clean image through the obtained noisedeviation and the given noisy image Due to the lack of ground-truth images in the real MR dataset the performance of theproposedmodel was tested qualitatively and quantitatively on one simulated T1-weightedMR image dataset and then expanded tofour real datasetse experimental results show that the proposed 3D-Parallel-RicianNet network achieves performance superiorto that of several state-of-the-art methods in terms of the peak signal-to-noise ratio structural similarity index and entropymetric In particular our method demonstrates powerful abilities in both noise suppression and structure preservation

1 Introduction

Medical image information is playing an increasingly im-portant role in disease diagnosis However during the imageacquisition process due to the improper actions of patientsor staff strong random noise will inevitably be generatedis noise not only reduces the resolution of the image butalso affects the precision of clinician diagnosis [1 2]

At present popular magnetic resonance (MR) imagingtechnology is commonly used as a medical imaging tech-nology for visualizing human tissues and organs It does notpose any radiation hazard unlike CT imaging [3] and itachieves multiaspect multiparameter and high-contrast-resolution images without bone artifacts However the

random noise will affect the inspection quality in clinicaldiagnosis as well as image processing and analysis tasks suchas image segmentation registration and visualizationHence solving the problem of MR image denoising iscritical

e purpose of image denoising is to remove back-ground noise and retain valuable information [4] Manyconventional filtering techniques are often used such asWiener filtering [5] bilateral filtering [6] and total variationfiltering [7] Yang and Fei proposed a multiscale waveletdenoising method based on the Radon transform to denoiseMR images [8] Phophalia et al mitigated the problem ofmedical image denoising by using rough set theory (RST)[9] Awate and Whitaker devised a Bayesian denoising

HindawiComputational Intelligence and NeuroscienceVolume 2021 Article ID 5577956 18 pageshttpsdoiorg10115520215577956

method and verified it on diffusion-weighted MR images[10] Satheesh et al developed an MR image denoising al-gorithm using the contourlet transform which achieved ahigher peak signal-to-noise ratio than the wavelet transform[11] Zhang et al used an improved singular value de-composition method to denoise simulated and real 3Dimages e experimental results showed that their methodwas superior to the existing denoising methods [12] Lealet al presented a method based on sparse representationsand singular value decomposition (SVD) for nonlocallydenoising MR images is method prevents blurring ar-tifacts and residual noise [13] In addition by extending thelocal region to a nonlocal scheme the nonlocal means(NLM) strategy was used for MR image denoising [14ndash16]Gautam et al proposed a novel denoising technique for MRimages based on the advanced NLM method with non-subsampled shearlet transform (NSST) [17] Kanoun et alproposed an enhanced NLM filter using the Kolmogorov-Smirnov (KS) distance e experimental results providedexcellent noise reduction and image-detail preservation [18]

In recent years the explosive development of deeplearning has suggested a new methodology for imagedenoising It can use multiple convolution filters to auto-matically extract features with large receptive fields toreconstruct high-resolution images In [19] the authors usedthe self-encoder to train the image features of differentresolutions to achieve adaptive denoising Zhang et alexploited denoising convolutional neural networks(DnCNNs) for Gaussian noise removal and achieved ex-cellent performance by using residual learning strategy [20]Cherukuri et al applied a deep learning network that lev-eraged the prior spatial structure of images to reconstructhigh-resolution images [21] Manjoprimen et al proposed a novelautomatic MR image denoising method by combining aconvolutional neural network (CNN) with a traditional filter[22]

Deep learning-based denoising methods can graspricher contextual information in large regions to improveperformance With very deep architectures it can expandthe receptive field of the network to capture more globalcontextual information over large image regions Liu et alutilized the multiscale fusion convolution network(MFCN) to perform super-resolution reconstruction ofMR images [23] Pham et al used a deep 3D CNN modelwith residual learning to reconstruct MR images [24] eirmodel exploited a very deep architecture with a large re-ceptive field to acquire a powerful learning ability Jianget al described a multichannel denoising convolutionalneural network (MCDnCNN) that directly learned theprocess of denoising and performed experiments onsimulation and real MR data [25] In [26] Ran et alsuggested a residual encoder-decoder Wasserstein gener-ated countermeasure network (RED-WGAN) for MRimage denoising Hong et al designed a spatial attentionmechanism to obtain the area of interest in MR imageswhich made use of the multilevel structure and boosted theexpressive ability of the network [27] Tripathi and Bagproposed a novel CNN for MR image denoising eproposed model consisted of multiple convolutions that

captured different image features while separating inherentnoise [28] Li et al designed a progressive network learningstrategy by fitting the distribution of pixel-level and fea-ture-level intensities eir experimental results demon-strated the great potential of the proposed network [29]Gregory et al created HydraNet a multibranch deep neuralnetwork architecture that learned to denoise MR images ata multitude of noise levels and proved the superiority ofthe network on denoising complex noise distributionscompared to some deep learning-based methods [30]Aetesam and Maji proposed a neural framework for MRimages denoising using an ensemble-based residuallearning strategy High metric value and high-quality visualresults were obtained in both synthetic and real noisydatasets [31]

In the above reported deep learning denoising tasks thedepth and width of the networks were often increased tocapture more contextual information However thesemethods introduced a number of parameters which made itdifficult to train the denoising models Some of the methodslearned the Rician noise distribution solely by stackingconvolution layers which easily overlooked much localinformation and led to unsatisfactory denoising results atsome key local anatomical positions

To address the above shortcomings this work proposesa novel network termed 3D-Parallel-RicianNet that is usedto remove the noise of MR images First to expand thereceptive field without introducing more parameters wedesign a dilated convolution residual (DCR) module anduse it to build a subnetwork (DCRNet) that can extractglobal information by cascading en a depthwise sepa-rable convolution residual (DSCR) module is designed andused to construct a subnetwork (DSCRNet) to extract localinformation Finally the features of each module ofDCRNet and DSCRNet are merged and cascaded to obtainfull-scale mappings between image appearances and noisedeviation

e main contributions of this work are summarized asfollows

(1) DCRNet expands the receptive field to extract richcontext information through cascading DCR mod-ules which capture the real Rician distribution in theglobal area

(2) DSCRNet uses the DSCR module to focus on thelocal area of the image and effectively removes localanatomical noise Each DSCR module of this sub-network is added to the output part of each DCRmodule of the corresponding DCRNet

(3) e 3D-Parallel-RicianNet uses a residual learningmechanism to prevent vanishing and explodinggradient problems

e remainder of this work is organized as follows InSection 2 we describe the proposed denoising networksand loss function en in Section 3 we present theexperimental tests of our approach on synthetic and realMR noisy data Additionally a comparison of our methodwith state-of-the-art algorithms is provided Finally in

2 Computational Intelligence and Neuroscience

Section 4 we discuss our conclusions and give futuredirections

2 Materials and Methods

21 Noise Reduction Model MR magnitude image is cor-rupted by independent Gaussian distribution noise in thereal part and the imaginary part of images [32ndash34] Previousstudies suggest that the probability distribution of noisy MRimage pixel intensity can be represented as a Rician dis-tribution [35 36] Deep learning can ignore the physicalprocess and model this procedure corruption by learningfrom the samples [26] Hence the MR image degradationmodel with noise can be described as

Y X + δ(Y) (1)

where Y is the noisy MR image X is the noise-free imageand δ(Y) is the deviation between X and Y influenced by theRician distribution According to equation (1) δ(Y) can beexpressed as (Y minus X) so it was employed to train a residualmapping f(YΘ) asymp δ(Y) and we can obtainX asymp Y minus f(YΘ) Figure 1 shows that the probabilitydensity distribution (PDF) of noisy MR images varies inglobal and local regions It can be seen from the top leftimage that the noise reduces the quality of theMR image andblurs the boundaries of some tissue structures which resultsin increased difficulty in recognizing the image details Liuet al pointed out that the PDFs of Rician noise vary spatiallyin different anatomical regions of brain MR images [37]Hence the nonlinear mappings between image appearancesand Rician distributions vary in global and local regionsBased on this conclusion we propose the 3D-Parallel-RicianNet MR image denoising model which combines theglobal and local feature information on global regions andlocal regions

22 DCR Module for Global Feature Representation It isknown that context information is important to reconstructcorrupted pixels for image denoising Specifically it is acommon way to capture more global context information byexpanding the receptive field [38] In the reported deeplearning denoising tasks increasing the depth and width ofthe deep networks can enlarge the receptive field Howeverthe width-adding methods may produce more parameterswhich results in overfitting of the network e depth-adding methods may lead to vanishing gradients when thedepth of the network is enormous

To solve these problems dilated convolutions have beendeveloped [39] e dilation rate of the convolution kernelcan be controlled to obtain receptive fields of different sizesas shown in Figure 2 e size of the receptive field v isdenoted as

v ksize minus 1( 1113857 times(R minus 1) + ksize( 1113857d (2)

where ksize is the size of the filterR is the dilated rate and d isthe dimension (2 or 3) of the imagee receptive field of theconvolution operation can be expanded by setting differentR is creates a tradeoff between increasing the depth and

width of CNNs In [40] Peng proposed dilated residualnetworks with symmetric skip connection (DSNet) eexperiments demonstrated that the model was more feasiblefor the task of image denoising especially for Gaussiannoise Zhang et al proposed a dual-domain multiscale CNN(DMCNN) for JPEG artifacts based on dilated convolutionis also proved that dilated convolution had advantages inrestoring image quality [41]

In this study we construct the DCR module as onecomponent of our 3D-Parallel-RicianNet It exploits dilatedconvolutions to extract global features as shown in Figure 3e DCR module consists of dilated convolution residuallearning batch normalization (BN) and leaky rectifiedlinear unit (LeakReLU) Residual learning fundamentallybreaks the symmetry of the network thereby improving theability of the representation network By setting the BNlayer the generalization ability of the network is improvedDue to the problem of vanishing gradients using the ReLUactivation function we use LeakReLU as the activationfunction of the network e input and output of a two-leveldilated convolution are briefly connected to construct a DCRmodule

23DSCRModule for Local Feature Representation It is veryimportant to recover the local fine details in imagedenoising When some local features are not well extractedthe local denoising effect will be degraded Recentlydepthwise separable convolution (DSConv) has been used inmany advanced neural networks such as Xception [42]MobileNets [43] and MobileNets2 [44] to replace thestandard convolutional layer aiming to reduce CNNcomputational cost and to extract local features [45]

DSConv consists of two parts depthwise convolutionand pointwise convolution As shown in Figure 4 thedepthwise convolution acts on each input channel sepa-rately to exact local features followed by a pointwiseconvolution that uses 1 times 11 times 1 times 1 convolution to weightthe features among channels at every point Hence thiswould efficiently extract the local features among differentchannels e input feature map is I I1 I2 In1113864 1113865 Firstusing depthwise convolutions with n filtersK K1 K2 Kn1113864 1113865 an intermediate result J J1 J21113864

Jn is produced which is then processed into the outputfeature mapO O1 O2 Om1113864 1113865 bymeans of the pointwiseconvolutions using m filters k k1 k2 km1113864 1113865

DSConv can extract local delicate features of the imageby considering the information of the position and channelseparately Imamura et al designed a denoising network forhyperspectral images using DSConv and demonstrated itsability to realize efficient restoration [46] e advantage ofDSConv is that it reduces the number of network parametersand the computational complexity in convolution opera-tions [42ndash44]

e model designed by using dilated convolution canrestore the image quality globally [40 41] but can easilyignore local information To solve this problem inspired byDSConv we extend the technique to the DSCR module toextract the local information of the MR images as shown in

Computational Intelligence and Neuroscience 3

Figure 5 We utilize the residual strategic idea and take thedepthwise separable convolutions as the main constructionmodule On the one hand we design two continuousdepthwise separable convolutions with the BN layer after

each convolution layer to improve the generalization abilityof the network On the other hand we use another depthwiseseparable convolution to shortcut the module to preventvanishing gradients

24 e Proposed 3D-Parallel-RicianNet Model e pro-posed 3D-Parallel-RicianNet framework consists of a globalfeature extraction network DCRNet a local feature ex-traction network DSCRNet and a reconstruction (REC)module Under this framework the pipeline of MR imagedenoising is composed of three major steps (see Figure 6)First we apply DCRNet and DSCRNet to extract the globalfeatures and local features respectively en we fuse the

Noisy MR image (160 times 192 times 160) Noisy MR image (12 voxels ) Noisy MR image (14 voxels) Noisy MR image (18 voxels)

The pixel distributionof all voxels0015 004

The pixel distributionof 12 voxels

005

The pixel distributionof 14 voxels 006


001003 004 005

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Figure 1 PDFs in different sizes of subwindowse height of each vertical bar is the proportion of the corresponding pixel valuee linesrepresent the fitted pixel distribution Top row from left to right a 3D T1-weightedMR image with 7 Rician noise a 12-voxel T1-weightedMR image a 14-voxel T1-weighted MR image and a 18-voxel T1-weighted MR image Bottom row PDFs are of intensity in the cor-responding voxels As shown the PDF (12 voxels) within the red region tends to be similar for the whole image However the PDFs in thesmall local green region (14 voxels) and local blue region (18 voxels) are different from those in the global region

3 times 3 Kernel

Dilated convolution(R = 1)

(a)

3 times 3 Kernel


(b)

3 times 3 Kernel


(c)

Figure 2 Dilated convolution (a) e receptive field of the convolution kernel of size 3 times 3 pixels which covers a 3 times 3 subregion in theimage through a convolution operation (b) e receptive field of the convolution kernel with an R of 2 (c) e receptive field of theconvolution kernel with an R of 3

Dila

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Figure 3 e structure of the DCR module


global and local features through an additional layer toobtain real Rician distribution features Finally we use theREC module to obtain a predicted clean MR image 1113954X

DCRNet e proposed DCRNet framework is a cascade of18 DCR modules with different R e kernel size is 3 times

33 times 3 times 3 for 2D slices3D patches Dilated convolutionwith a large R behaves well for low-frequency noise removalWhen R is too large it is difficult to capture some smallcontextual information which will cause the waste of re-ceptive fields If R is 1 it is the same as the traditionalconvolution in each channel In DCRNet to ensure that allfeature maps have the same size as the input we symmet-rically pad zeros around the boundaries before applying theconvolution operation As the convolutional layer increasesthe range of the receptive field will gradually increase Inaddition a gridding problem is known to exist in dilated

convolution [47] To solve these problems considering thesize of the input in our experiments we applied DCRmodules with different dilation rates erefore the dilatedrate of each layer is set to 1 1 1 1 1 1 2 3 1 2 3 1 2 3 1 23 and 1 e final receptive field is 61 Multiscale globalfeatures are extracted by using multiple DCR modules withdifferent dilation rates Each module has 16 filters eimplementations can avoid the gridding effects and reducethe influence of unrelated information

DSCRNet DSCRNet is further used to compensate for thelocal information ignored by expanding the receptive field Itis a cascade of 18 DSCRmodulese size of the convolutionkernel of each module is 3 times 33 times 3 times 3 Each module alsohas 16 filters

We fused the features extracted from each module ofDCRNet and DSCRNet to gradually realize the complemen-tarity of global and local information is process particularlyhelps to preserve critical image features in global regions andlocal regions erefore the proposed 3D-Parallel-RicianNetmodel will have better denoising ability than other methods

REC Module After a convolution layer we obtain theestimated deviation f(YΘ) and then use 1113954X Y minus f(YΘ)

to obtain a predicted clean MR image

25 Loss Function Our loss function uses the mean squarederror (MSE) as follows

ι(Θ) 1N

1113944

N

i1Yi minus f YiΘ( 1113857 minus X

2i (3)

where Xi is the ith noise-free image Yi is the corresponding

noisy image and Θ denotes the network parameters Weminimize this loss function to learn the output noise-freeimage (Yi minus f(YiΘ))

3 Experiments Results and Analysis

31 Dataset Description To validate the performance of theproposed 3D-Parallel-RicianNet extensive experiments

I1

Input Output

Depthwise convolutional kernel

Pointwise convolutional kernel

I2

In

K1

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Kn

J1

J2

Jn

k1

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km

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Figure 4 Depthwise separable convolutions (DSConv)

Depthwise separable convolutions (DSCov)Kernel (3 times 3) (3 times 3 times 3)

Add


BN

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Figure 5 e structure of the DSCR module


were performed on both public simulated and clinicaldatasets

For simulated experiments the BrainWeb dataset[48 49] was used In this work we obtained 18 T1-weighted(T1w) MR images with different noise levels (1 3 57 and 9)e size of the image is 181 times 217 times 181 and itsresolution is 1 times 1 times 1mm3e brain skull is stripped by theskull mask To further speed up the training process andobtain fewer redundant areas we cropped the edges of theimage and the image size is 160times192times160

One critical problem of the deep learning approach isweak generalization applicability Networks trained on onedataset from a specific manufacturer or setting may notperform well for a different dataset e noise in the sim-ulation dataset is assumed to come from single coil acqui-sition systems However clinical MR image noisedistributions come from multiple coils and these noisesare subject to a noncentral Chi distribution with a sum-of-squares (SoS) reconstruction Actually the Rician dis-tribution is a special case of the noncentral Chi distribution[50] and varies spatially in real MR images [37]

To verify the generalization ability of the proposedmodel we carried out experiments on real datasets For thefirst clinical experiment the well-known IXI dataset [51] wasused which was collected from 3 different hospitals Werandomly selected 100 T1w brain images from the Ham-mersmith dataset e image size is 256 times 256 times 150 and thevoxel resolution is 09375 times 09375 times 12mm3 Sixty imageswere randomly selected as the training set 20 images forvalidation and the other 20 images for testing In thisdataset we manually added different levels of Rician noise tosimulate the noisy image [26] e brain skull was strippedby the VolBrain method [52]

For another experiment we randomly selected 35 T1wimages in ADNI [53] Each of these samples contained 192 times

192 times 160 voxels with 12 times 125 times 125mm3 voxel resolu-tion For the experiment the original scan was resized todimensions of 256 times 256 times 128 e brain skull was alsostripped by the VolBrain method Due to the lack ofknowledge about the noise level in real data we used thevariance-stabilization approach to estimate the Rician noise

level of ADNI data which was approximately 3 [54]Hence we selected IXI models trained with a 3 noise levelto test ADNI data

e last dataset comes from the Combined HealthyAbdominal Organ Segmentation (CHAOS) challenge[55 56]e dataset included 40 abdominal T1wMR imagesOn average each volume size is 256 times 256 times 36 and thenoise level is unknown We adjusted the image to256times 256times 64 through zero-padding operations to be uni-form To substantiate the robustness and generalizationcapability of the proposed framework we employed thisdataset for our experiments splitting it into subsets of 25 5and 10 subjects that were used for training validation andtesting

32 Training Details We use two strategies for training onthe three datasets of BrainWeb IXI-Hammersmith andCHAOS 2D slice-based training and 3D patch-basedtraining For 2D training we extracted 2D coronal slicesfrom 3D data in the BrainWeb dataset We obtained 2880slices by rotating 90deg and mirroring with 1920 slices fortraining 384 slices for validation and 576 slices for testingIn the IXI-Hammersmith dataset we cropped the image to256times 256times128 and tested it in all clinical brain datasets Weextracted 7680 slices for training 2560 slices for validationand 2560 slices for testing in the sagittal plane In theCHAOS dataset using rotation and mirroring to expand thedata we obtained 6400 sagittal slices for training 1280sagittal slices for validation and 640 sagittal slices for testing

For patch-based training 3D data in the BrainWebdataset was also expanded by rotation and mirroring Toreduce memory burden we used patches with a size of64times 64times 64 voxels A sliding window strategy with a strideof 16 times 32 times 16 was then used to obtain 3675 patches to trainthe 3D model Using the same strategy as the BrainWebdataset 4500 training patches 1500 validation patches and1500 test patches were extracted from IXI-Hammersmithwith a step size of 48 times 48 times 32 We used rotating andmirroring to expand the CHAOS dataset before extractingpatches and finally obtained 4900 training patches 980

DCR

(R =

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Xf (Y Θ)

Figure 6 e proposed network architecture for MR image denoising


validation patches and 490 test patches with a stride of32 times 32 times 64 In the training stage since the CHAOS datasetdid not have clean images and the noise level was unknownwe used the 5 noise model trained by IXI-Hammersmith toestimate clean images as ground truth In the testing stagewe applied the trained network to patches of the test set eresultant predictions were averaged in the overlappingregions

All training was conducted using a deep learning ac-celeration computing service which is configured with a220GHz Core i7-8750H CPU an NVIDIA GeForce GTX1070 (8G) GPU and 16GB RAM All the deep learningmodels were implemented with the publicly available Ten-sorFlow framework and Keras artificial neural network li-brary In the training process the learning rate was set to 1e-3 We used Adam optimization

33 Evaluation Methods Six kinds of deep learning modelswere trained CNN-DMRI [28] RicianNet [29] 2D-DCRNet 2D-Parallel-RicianNet 3D-DCRNet and 3D-Parallel-RicianNet We compared these six deep learningmodels with four traditional denoising methods NLMBM3D ODCT3D [57] and PRI-NLM3D [57] In the NLMmethod the fastNLMMeansDenoising function is selectedwhere the template size is 7 times 7 and the filter strength is 15

ree quantitative metrics were employed to evaluate thedenoising performance of these methods e first was thepeak signal-to-noise ratio (PSNR) A high PSNR generallydenotes good denoising performance e second was thestructural similarity index (SSIM) which measured thestructural similarity between the ground-truth and denoisedimages e last one was entropy which reflected theamount of image information We used the natural loga-rithm in the entropy metric

34 Simulated Results e quantitative results of NLMBM3D ODCT3D PRI-NLM3D CNN-DMRI 2D-DCRNet 2D-Parallel-RicianNet 3D-DCRNet and 3D-Parallel-RicianNet on T1w images with different noiselevels (1 3 5 7 9) are illustrated in Tables 1ndash3

Tables 1 and 2 depict the PSNR and SSIM results re-spectively We can observe that the PSNR values of 3D-Parallel-RicianNet are obviously higher than those of theother methods at all noise levels In Table 2 the SSIM valuesof 3D-Parallel-RicianNet are closer to 1 which is higher thanthose of the other methods under all noise levels except PRI-NLM3D at the 7 noise level is indicates that ourproposed model has good denoising performance with goodanatomical structure preservation

Table 3 shows the entropy results of 10 methods We findthat the proposed 3D-Parallel-RicianNet can obtain thelowest entropy under all five noise levels Hence consideringthe three metrics in 3 tables we find that our method hasbetter noise reduction performance In addition to visualquality another important aspect of theMR image denoisingmethod is the time complexity We give running times fordifferent methods in Table 4 It is clear that 3D-DCRNet andour proposed 3D-Parallel-RicianNet are much faster than

other methods Once the deep learning-based method fin-ishes training forward propagation is very fast In Table 5our method has the fewest parameters whichmeans that ournetwork does not need too much computational powerFrom this we can see that our model has competitive ad-vantages for small data sets

Figures 7 and 8 provide a visual comparison for T1wimages from testing data under 3 and 9 noise levels using10 methods e zoomed-in regions of the denoised imagesare shown to observe noticeable details In Figure 7 allmethods can achieve good performance under low-levelnoise circumstances However traditional methods sufferfrom obvious oversmoothing effects and distort someimportant details Among deep learning methods theimages processed by CNN-DMRI 2D-DCRNet 2D-Parallel-RicianNet and 3D-DCRNet have obvious Riciannoise RicianNet increases the brightness of the brain areaand makes it difficult to clearly observe the anatomicalstructure Figure 7 shows that the 3D-Parallel-RicianNetdenoising method gives better results and preserves thekey information in the image

While the noise level increases the traditional methodssuffer from obvious oversmoothing effects as shown inFigure 8 CNN-MRI and RicianNet models still have somenoise and suffer from slight oversmoothing of texturedregions By using the DCR module 2D-DCRNet and 3D-DCRNet have a strong denoising ability globally for 2D slice-based and 3D patch-based cases However without con-sidering local structural features the DCRNet model losessome important local details in the denoising processHence by combining global features of DCRNet and localfeatures of DSCRNet the proposed 3D-Parallel-RicianNetcan preserve finer detailed structures in homogeneous areasand it obtains the most consistent results with noise-freeimages Hence our 3D-Parallel-RicianNet method canbetter retain the key information in denoised MR imageswhich is useful for improving the precision of cliniciandiagnosis

35 Clinical Results

351 Results from the IXI-Hammersmith Dataset To vali-date the performance of the proposed 3D-Parallel-RicianNetten denoising methods were compared on different clinicaldata sets

Figures 9ndash11 summarize the three metrics in the IXI-Hammersmith dataset with 10 methods under differentnoise levels At a noise level of 1 the PRI-NLM algo-rithm achieves denoising performance comparable to thatof 3D-Parallel-RicianNet in terms of PSNR At noise levelsabove 5 the proposed model produces higher PSNRsthan the competing methods In particular in Figure 10we can see that the 3D-Parallel-RicianNet model con-sistently yields SSIMs higher than the other nine methodsfor all noise levels From the perspective of entropy ourmethod had a low entropy value ese results indicatedthat the 3D-Parallel-RicianNet model had a strongdenoising ability


Figure 12 shows an example of denoising results using 10methods on the IXI-Hammersmith dataset with 3 noise Itcan be seen in the figure that the proposed 3D-Parallel-RicianNet model gives the best denoising results and thedenoised image is virtually identical to the ground-truth imageAfter visual inspection it can be deduced that the outcome ofour proposed 3D-Parallel-RicianNet is improved compared tothe others in terms of fine-structure retention and edges

352 Results from the IXI-Guys Dataset Figures 13ndash15summarize the PSNR SSIM and entropy values using 10methods on the IXI-Guys dataset We test the trained model

with the IXI-Hammersmith dataset on this IXI-Guysdataset which reflects network generalization on othernontrained datasets e 3D-Parallel-RicianNet shows themost robust performance among the tested methods interms of PSNR SSIM and entropy In particular our modelstill achieves better denoising ability than other methods athigher noise levels

Figure 16 shows an example of denoising results ob-tained with 10 methods on data from the IXI-Guys dataset atthe 3 noise level Consistent with the denoising perfor-mance on the IXI-Hammersmith dataset the proposed 3D-Parallel-RicianNet method provided the best denoising re-sult and removed the image noise more robustly than theother methods on the IXI-Guys dataset Particularly in theregion indicated by the red line the 3D-Parallel-RicianNetmodel achieved better visual results

353 Results from the ADNI Dataset is subsection isdevoted to verifying the consistency of the proposed ap-proach on the ADNI dataset Because noise-free images areunavailable entropy is measured and used as the quanti-tative metric e results are shown in Figures 17 and 18

As shown in Figure 17 although the RicianNet and 2D-DCRNet remove noise they suffer from obvious over-smoothing effects and it is difficult to identify the keyanatomical structures In addition the denoising effect is notsatisfactory when using BM3D ODCT3D PRI-NLM3DCNN-DMRI 2D-Parallel-RicianNet and 3D-DCRNet eresults of these methods still contain substantial noise andmiss some of the structural details It can be noted that 3D-Parallel-RicianNet retains the details better than othermethods

According to Figure 18 the entropy results of denoisedMR images in the ADNI dataset using different processingmethods are compared We find that 3D-Parallel-RicianNet

Table 1 PSNRs on different noise levels from BrainWeb datasetwith 10 methods

Methods 1 3 5 7 9NLM 341381 321259 299717 294599 278319BM3D 353151 331937 310144 304890 289093ODCT3D 481295 362756 315857 305124 282452PRI-NLM3D 498923 368192 319597 309418 285961CNN-DMRI 478125 354720 308958 293533 272152RicianNet 434145 370095 274807 276777 2886162D-DCRNet 468168 386786 346277 324664 3052322D-Parallel-RicianNet 509072 418099 388218 359767 345207

3D-DCRNet 485120 391336 351466 327280 3109163D-Parallel-RicianNet 517192 439950 409218 376896 371069

Table 2 SSIMs on different noise levels from BrainWeb datasetwith 10 methods

Methods 1 3 5 7 9NLM 09669 09605 09539 09521 09454BM3D 09768 09725 09673 09649 09584ODCT3D 09992 09959 09903 09857 09778PRI-NLM3D 09995 09967 09922 09889 09823CNN-DMRI 09987 09891 09727 09533 09312RicianNet 09606 08906 09221 07246 063192D-DCRNet 09986 09900 09906 09535 093462D-Parallel-RicianNet 09992 09933 09864 09685 097223D-DCRNet 09985 09898 09587 09561 093733D-Parallel-RicianNet 09995 09982 09942 09883 09859

Table 3 Entropy on different noise levels from BrainWeb datasetwith 10 methods

Methods 1 3 5 7 9Noisy image 24787 25067 25266 25482 25556NLM 24721 24581 24474 24470 24324BM3D 24532 24476 24849 24676 24803ODCT3D 24516 24844 24988 25102 25033PRI-NLM3D 24447 24415 24291 24330 24201CNN-DMRI 24499 24869 25086 25313 25406RicianNet 24629 24715 24519 24511 246062D-DCRNet 24624 24701 24742 23481 241422D-Parallel-RicianNet 24693 23995 24073 24631 213743D-DCRNet 24556 24488 24331 23340 217873D-Parallel-RicianNet 24364 23469 23275 22890 20642

Table 4 Execution time on different noise levels from BrainWebdataset with 10 methods

Methods 1 3 5 7 9 AverageNLM 1055 1054 1058 1054 1055 1055BM3D 2826 2813 2729 2737 2825 2786ODCT3D 2354 1756 1802 1475 1454 1768PRI-NLM3D 1407 1250 1292 1359 1328 1327CNN-DMRI 113 111 113 112 112 112RicianNet 171 165 165 169 166 1672D-DCRNet 127 132 134 133 129 1312D-Parallel-RicianNet 118 114 113 112 112 114

3D-DCRNet 094 092 091 091 092 0923D-Parallel-RicianNet 089 089 089 089 089 089

Table 5 Number of parameters of different networks

Method CNN-DMRI RicianNet 3D-Parallel-

RicianNetNumber ofparameters 1444929 5346114 395405


achieves the lowest entropy value Combined with Figure 17we find that our method not only effectively removes noisebut also preserves more useful key information in imagesHence our 3D-Parallel-RicianNet method has strong gen-eralization ability and strong robustnessese experimentalresults once again demonstrate the advantages of our pro-posed model

354 Denoising of Real Abdominal MR Data In this sub-section we performed denoising for abdominal MR imagesby the proposed network We compared three denoisingmethods and the experimental results are shown in Table 6

Table 6 shows that the PSNR of our method can reach397090 which is higher than those of BM3D CNN-DMRIand RicianNet On SSIM RicianNet is lower than BM3D and

(a) (b) (c) (d) (e) (f)

(g) (h) (i) (j) (k) (l)

Figure 7 Denoising effect of different methods with 3 noise level (a) Noisy image (b) noise-free image (c) NLM (d) BM3D(e) ODCT3D (f ) PRI-NLM3D (g) CNN-DMRI (h) RicianNet (i) 2D-DCRNet (j) 2D-Parallel-RicianNet (k) 3D-DCRNet (l) 3D-Parallel-RicianNet

(a) (b) (c) (d) (e) (f)

(g) (h) (i) (j) (k) (l)



CNN-DMRI indicating that although RicianNet canremove noise it cannot retain the structure information ofthe image Our method can still obtain the highest SSIMvalue We show the denoising results of the four methods inFigure 19 It can be seen from the figure that our method cannot only remove noise but also preserve the key anatomicalposition information in the image completely

36 Comparisons of the Results with Different SpatialResolutions e image resolution affects the quality of theimage Generally when the image resolution is smaller thedenoising ability of the model is significantly reduced In thispart we use the BrainWeb dataset to verify the denoisingeffect of images with different resolutions at a noise level of3 e results are shown in Table 7

From Table 7 it can be observed that the proposed 3D-Parallel-RicianNet outperforms other methods tested amongthe different spatial resolutions For BM3D and RicianNet theyare difficult to remove noise at low spatial resolutions It isnoted that noise cleaning appears to have a consistent effectwhen different spatial resolutions are relatively close such as09375 times 09375 times 09375mm3 and 1 times 1 times 1mm3 However itshould be noted that some loss of contrast and spatial reso-lution is possible Once the difference between the resolutionsbecomes larger the denoising effect will also change signifi-cantly such as 1 times 1 times 1mm3 and 2 times 2 times 2mm3 In additionthe PSNRs of deep learningmethods decrease significantly withdecreasing spatial resolution while the SSIM values are rela-tively close indicating that deep learningmethods recovermostof the complex anatomical structures Compared to othermethods our model has a more balanced denoising ability atdifferent spatial resolutions and the mean value of PSNR canreach 416373 Since the proposed 3D-Parallel-RicianNet canextract the global and local features in the noisy image andrestore the clean image it can still maintain denoising ability atlow spatial resolution

37 Comparisons of the Results with Different Brain TissuesBased on MR imaging technique key brain tissues likegray matter (GM) white matter (WM) and cerebrospinal

1 3 5 7 9

25

30

35

40

45

50PS

NR

(dB)

Noise level ()

NLMBM3DODCT3DPRI-NLM3DCNN-DMRI

RicianNet2D-DCRNet2D-Parallel-RicianNet3D-DCRNet3D-Parallel-RicianNet

Figure 9 PSNRs using 10 methods under different noise levels forthe IXI-Hammersmith dataset

085

090

095

100

SSIM

1 3 5 7 9Noise level ()



Figure 10 SSIMs using 10 methods under different noise levels forthe IXI-Hammersmith dataset

1 3 5 7 90

1

2

3

4

5

Entr

opy

Noise level ()

NLMBM3DODCT3DPRI-NLM3DCNN-DMRIRicianNet

2D-DCRNet2D-Parallel-RicianNet3D-DCRNet3D-Parallel-RicianNetNoisy image

Figure 11 Entropy using 10 methods under different noise levelsfor the IXI-Hammersmith dataset


1 3 5 7 920

25

30

35

40

45

50

PSN

R (d

B)

Noise level ()



Figure 13 PSNRs using 10 methods under different noise levels for the IXI-Guys dataset

(a) (b) (c) (d) (e) (f)

(g) (h) (i) (j) (k) (l)

Figure 12 e denoising effect for IXI-Hammersmith dataset with different methods at 3 noise level (a) Noisy image (b) noise-freeimage (c) NLM (d) BM3D (e) ODCT3D (f ) PRI-NLM3D (g) CNN-DMRI (h) RicianNet (i) 2D-DCRNet (j) 2D-Parallel-RicianNet(k) 3D-DCRNet (l) 3D-Parallel-RicianNet Each method below shows the corresponding edge detection image of the enlarged area (green)and the yellow represents the overlapping area with the noise-free image (red)


fluid (CSF) become visible ese three tissues help vi-sualize brain structures and guide surgery but noise canaffect the interpretation of brain tissue [58] To evaluatethe denoising effectiveness of 3D-Parallel-RicianNet ondifferent brain tissues state-of-the-art methods BM3DCNN-DMRI and RicianNet are compared in Table 8 eproposed model can achieve better PSNR and SSIM

results than the competing methods in different braintissues In particular in CSF we can see that the PSNR of3D-Parallel-RicianNet can reach 519105 We also showthe different brain tissue denoising results of fourdenoising methods in Figure 20 ese experimental re-sults once again demonstrate the advantages of the pro-posed model




0

1

2

3

4

5

Entr

opy

Figure 15 Entropy using 10 methods under different noise levels for the IXI-Guys dataset

1 3 5 7 9

080

085

090

095

100

Noise level ()

SSIM



Figure 14 SSIMs using 10 methods under different noise levels for the IXI-Guys dataset


38 Variants of the R Setting in the DCR Module In ourmodel the DCR module of different R is our key componente PSNR and SSIM are recorded in Table 9 by different R

settings at the 3 noise level in the BrainWeb dataset Weconducted three experiments each using the same dilation ratefor the 18 DCR modules e final receptive fields are 37 73and 109 Combining Tables 1 and 2 and Table 8 we can find

that our hybrid dilation rate can reach the highest PSNR andSSIMWhenR 2 and 3 the receptive field has already causedwaste In addition using the same dilation rates can easily causegridding effects ere is a lack of correlation between thefeature maps extracted in this way and an accurately predictedresult cannot be obtained in the enderefore our model canachieve superior denoising performance

(a) (b) (c) (d) (e) (f )

(g) (h) (i) (j) (k)

Figure 17 e denoising effect of ADNI set with different methods at 3 noise level (a) Noisy image (b) NLM (c) BM3D (d) ODCT3D(e) PRI-NLM3D (f ) CNN-DMRI (g) RicianNet (h) 2D-DCRNet (i) 2D-Parallel-RicianNet (j) 3D-DCRNet (k) 3D-Parallel-RicianNet

(a) (b) (c) (d) (e) (f )

(g) (h) (i) (j) (k) (l)

Figure 16 e denoising effect for IXI-Guys dataset with different methods at 3 noise level (a) Noisy image (b) noise-free image(c) NLM (d) BM3D (e) ODCT3D (f ) PRI-NLM3D (g) CNN-DMRI (h) RicianNet (i) 2D-DCRNet (j) 2D-Parallel-RicianNet (k) 3D-DCRNet (l) 3D-Parallel-RicianNet


(a) (b) (c)

(d) (e) (f )

Figure 19 e denoising effect of CHAOS set with different methods at 3 noise level (a) Noisy image (b) noise-free image (c) BM3D(d) CNN-DMRI (e) RicianNet (f ) 3D-Parallel-RicianNet

18

17

16

15

14En

tropy

NLM

BM3D

OD

CT3D

PRI-

NLM

3D

CNN

-DM

RI

Rici

anN

et

2D-D

CRN

et

2D-P

aral

lel-R

icia

nNet

3D-D

CRN

et

3D-P

aral

lel-R

icia

nNet

Noi

sy im

age

Figure 18 e entropy of the denoised images from the ADNI database

Table 6 e PSNR and SSIM on different noise levels from CHAOS dataset with 4 methods

Method BM3D CNN-DMRI RicianNet 3D-Parallel-RicianNetPSNR 319167 320655 352577 397090SSIM 09862 09867 09258 09941


4 Discussion and Conclusions

In this work we propose a parallel denoising residualnetwork based on cascaded DCR and DSCR modules to

address the random noise in MR images e global andlocal features are extracted by the designed DCRNet andDSCRNet and then these features are fused together Henceglobal and local information is captured to drive thedenoising progress of brain MR images by supervisednetwork learning

e PSNR SSIM and entropy are calculated to comparethe proposed method with many existing methods and thedenoising effect of the proposed method is verified on the

Table 7 PSNR (top) and SSIM (bottom) comparisons of different algorithms with different spatial resolutions

Spatial resolutions (mm3)Method

BM3D CNN-DMRI RicianNet 3D-Parallel-RicianNet09 times 09 times 09 318908 09709 347330 09890 357466 09233 415169 0997009375 times 09375 times 09375 321794 09718 352350 09903 364030 09117 419756 099731 times 1 times 1 331937 09725 354720 09891 370095 08906 439950 0998211 times 11 times 11 317986 09677 356006 09917 366172 09078 422193 09976125 times 125 times 125 313591 09633 340402 09917 360542 09070 419259 0997415 times 15 times 15 298656 09481 351568 09918 314012 09180 403297 099612 times 2 times 2 282362 09230 345695 09900 234731 09038 384990 09933

Figure 20 e denoising effect of brain tissues with different methods at 3 noise level Noisy image (1st column) noise-free image (2nd

column) BM3D (3rd column) CNN-DMRI (4th column) RicianNet (5th column) 3D-Parallel-RicianNet (6th column)

Table 8 PSNR and SSIM comparisons of different methods in different brain tissues

MethodCSF GM WM

PSNR SSIM PSNR SSIM PSNR SSIMBM3D 270765 09213 191709 09114 182741 09350CNN-DMRI 458322 09981 391790 09976 387420 09973RicianNet 448454 09982 419853 09988 436082 099863D-Parallel-RicianNet 519105 09996 475288 09996 486238 09998

Table 9 PSNR and SSIM comparisons in different R settings

R 1 R 2 R 3PSNR 410253 404788 393627SSIM 09956 09661 09946


BrainWeb simulation data under different noise levels Totest the practicability of the proposed network experimentson real clinical MR images show that the proposedmethod issuperior to other methods for the IXI-Hammersmith IXI-Guys ADNI and CHAOS datasets

In this work one of our limitations is that althoughstructural information can be retained at high noise levelsthere is still a small amount of local noise as shown inFigure 8 Next we will continue to study to find a balancebetween noise removal and structure maintenance at dif-ferent noise levels Another critical limitation of our methodis the requirement for high-quality noise-free ground-truthimages which are difficult to obtain in real applicationsIncorporation of prior knowledge about organ shape andlocation is key to improving the performance of imageanalysis approaches However in most recently developedmedical image analysis techniques it is not obvious how toincorporate such prior knowledge [59] Oktay et al incor-porated anatomical prior knowledge into a deep learningmethod through a new regularization model and thismethod showed that the approach can be easily adapted todifferent medical image analysis tasks (eg image en-hancement and segmentation) [59] Furthermore in [60]the author used morphological component analysis (MCA)to decompose noisy images into cartoon texture and re-sidual parts that were considered noise componentserefore to circumvent the limitations of our method wewill verify it using multimodality images and incorporateother meaningful priors such as residual parts organ shapeand location to mitigate semisupervised denoising tasks inthe future

In conclusion the results obtained in this paper areencouraging and efficiently demonstrate the potential of our3D-Parallel-RicianNet method for MR image denoisingis method can not only effectively remove noise in MRimages but also preserve enough detailed structural infor-mation which can help to provide high-quality MR imagesfor clinical diagnosis

Data Availability

eBrainWeb IXI ADNI and CHAOS datasets are publiclyavailable (BrainWeb httpsbrainwebbicmnimcgillcabrainweb IXI httpbrain-developmentorgixi-datasetADNI httpadniloniuscedu and CHAOS httpschaosgrand-challengeorg)

Conflicts of Interest

e authors declare no conflicts of interest

Acknowledgments

Data collection and sharing for this project was funded bythe Alzheimerrsquos Disease Neuroimaging Initiative (ADNI)(National Institutes of Health Grant U01 AG024904) andDOD ADNI (Department of Defense award numberW81XWH-12-2-0012) is research was supported in partby the National Natural Science Foundation of China under

Grant 61771230 the Shandong Provincial Natural ScienceFoundation under Grant ZR2016FM40 the ShandongProvincial Jinan Science and Technology Project underGrant (201816082 and 201817001) and the Youth Programof Shandong Provincial Natural Science Foundation underGrant ZR2020QF011

References

[1] Z Zhang D Xia X Han et al ldquoImpact of image constraintsand object structures on optimization-based reconstructionrdquoin Proceedings of the 4nd International Conference on ImageFormation in X-Ray Computed Tomography pp 487ndash490Bamberg Germany January 2016

[2] J Mohan V Krishnaveni and Y Guo ldquoA survey on themagnetic resonance image denoising methodsrdquo BiomedicalSignal Processing and Control vol 9 pp 56ndash69 2014

[3] J D Kumar and V Mohan ldquoEdge detection in the medicalMR brain image based on fuzzy logic techniquerdquo in Pro-ceedings of the International Conference on InformationCommunication and Embedded Systems (ICICES2014)pp 1ndash9 Chennai India February 2014

[4] K Gupta and S K Gupta ldquoImage denoising techniques areview paperrdquo International Journal of Innovative Technologyamp Exploring Engineering vol 2 no 4 pp 6ndash9 2013

[5] H M Ali ldquoMRI medical image denoising by fundamentalfiltersrdquo in High-Resolution Neuroimaging-Basic PhysicalPrinciples and Clinical Applications A M Halefoglu Edpp 111ndash124 InTech Zagreb Croatia 2018

[6] K N Chaudhury and S D Dabhade ldquoFast and provablyaccurate bilateral filteringrdquo IEEE Transactions on ImageProcessing vol 25 no 6 pp 2519ndash2528 2016

[7] L I Rudin S Osher and E Fatemi ldquoNonlinear total variationbased noise removal algorithmsrdquo Physica D NonlinearPhenomena vol 60 no 1-4 pp 259ndash268 1992

[8] X Yang and B Fei ldquoA wavelet multi-scale denoising algo-rithm for magnetic resonance (MR) imagesrdquo MeasurementScience and Technology vol 22 no 2 Article ID 025803 2011

[9] A Phophalia A Rajwade and S K Mitra ldquoRough set basedimage denoising for brain MR imagesrdquo Signal Processingvol 103 pp 24ndash35 2014

[10] S P Awate and R T Whitaker ldquoFeature-preserving MRIdenoising a nonparametric empirical Bayes approachrdquoIEEE Transactions on Medical Imaging vol 26 no 9pp 1242ndash1255 2007

[11] S Satheesh and K V S V R Prasad ldquoMedical imagedenoising using adaptive threshold based on contourlettransformrdquo 2011 httpsarxivorgabs11034907

[12] X Zhang Z Xu N Jia et al ldquoDenoising of 3D magneticresonance images by using higher-order singular value de-compositionrdquo Medical Image Analysis vol 19 no 1pp 75ndash86 2015

[13] N Leal E Zurek E Leal and Esmeide ldquoNon-Local SVDdenoising of MRI based on sparse representationsrdquo Sensorsvol 20 no 5 p 1536 2020

[14] H V Bhujle and B H Vadavadagi ldquoNLM based magneticresonance image denoising - a reviewrdquo Biomedical SignalProcessing and Control vol 47 pp 252ndash261 2019

[15] J Hu Y Pu X Wu Y Zhang and J Zhou ldquoImproved DCT-based nonlocal means filter for MR images denoisingrdquoComputational and Mathematical Methods in Medicinevol 2012 Article ID 232685 14 pages 2012


[16] X Zhang G Hou J Ma et al ldquoDenoising MR images usingnon-local means filter with combined patch and pixel simi-larityrdquo PLoS One vol 9 no 6 Article ID e100240 2014

[17] A Gautam and M M Mathur ldquoImplementation of NLM andPNLM for de-noising of MRI imagesrdquo International Journalof Computer Science and Mobile Computing vol 8 no 11pp 31ndash37 2019

[18] B Kanoun M Ambrosanio F Baselice G FerraioliV Pascazio and L Gomez ldquoAnisotropic weighted KS-NLMfilter for noise reduction in MRIrdquo IEEE Access vol 8pp 184866ndash184884 2020

[19] K G Lore A Akintayo and S Sarkar ldquoLLNet a deepautoencoder approach to natural low-light image enhance-mentrdquo Pattern Recognition vol 61 pp 650ndash662 2017

[20] K Zhang W Zuo Y Chen D Meng and L Zhang ldquoBeyonda Gaussian denoiser residual learning of deep CNN for imagedenoisingrdquo IEEE Transactions on Image Processing vol 26no 7 pp 3142ndash3155 2017

[21] V Cherukuri T Guo S J Schiff et al ldquoDeepMR brain imagesuper-resolution using spatio-structural priorsrdquo IEEETransactions on Image Processing vol 29 pp 1368ndash13832020

[22] J V Manj n and P Coupe oldquoMRI denoising using deeplearning and nonlocal averagingrdquo 2019 httpsarxivorgabs191104798

[23] C Liu X Wu X Yu et al ldquoFusing multiscale information inconvolution network for MR image super-resolution recon-structionrdquo Biomedical Engineering Online vol 17 no 1p 114 2018

[24] C H Pham A Ducournau R Fablet et al ldquoBrain MRIsuper-resolution using deep 3D convolutional networksrdquoin Proceedings of the IEEE International Symposium onBiomedical Imaging IEEE pp 197ndash200 Melbourne Aus-tralia April 2017

[25] D Jiang W Dou L Vosters X Xu Y Sun and T TanldquoDenoising of 3D magnetic resonance images with multi-channel residual learning of convolutional neural networkrdquoJapanese Journal of Radiology vol 36 no 9 pp 566ndash5742018

[26] M Ran J Hu Y Chen et al ldquoDenoising of 3D magneticresonance images using a residual encoder-decoder Was-serstein generative adversarial networkrdquo Medical ImageAnalysis vol 55 pp 165ndash180 2019

[27] D Hong C Huang C Yang et al ldquoFFA-DMRI A networkbased on feature fusion and attention mechanism for brainMRI denoisingrdquo Frontiers in Neuroscience vol 14 Article ID577937 2020

[28] P C Tripathi and S Bag ldquoCNN-DMRI a convolutionalneural network for denoising of magnetic resonance imagesrdquoPattern Recognition Letters vol 135 pp 57ndash63 2020

[29] S Li J Zhou D Liang and Q Liu ldquoMRI denoising usingprogressively distribution-based neural networkrdquo MagneticResonance Imaging vol 71 pp 55ndash68 2020

[30] S Gregory Y Gan H Cheng et al ldquoHydraNet a multi-branch convolutional neural network architecture for MRIdenoisingrdquo Medical Imaging 2021 Image Processingvol 11596 2021

[31] H Aetesam and S K Maji ldquoNoise dependent training fordeep parallel ensemble denoising in magnetic resonanceimagesrdquo Biomedical Signal Processing and Control vol 66Article ID 102405 2021

[32] J Yang J Fan D Ai S Zhou S Tang and Y Wang ldquoBrainMR image denoising for Rician noise using pre-smooth non-

local means filterrdquo Biomedical Engineering Online vol 14no 1 p 2 2015

[33] L He and I R Greenshields ldquoA non-local maximum like-lihood estimation method for Rician noise reduction in MRimagesrdquo IEEE Transactions on Medical Imaging vol 28 no 2pp 165ndash172 2008

[34] T Kalaiselvi and N Kalaichelvi ldquoInvestigation on imagedenoising techniques of magnetic resonance imagesrdquo Inter-national Journal of Computer Sciences and Engineering vol 6no 4 pp 104ndash111 2018

[35] S Aja-Fernandez C Alberola-Lopez and C-F WestinldquoNoise and signal estimation in magnitude MRI and riciandistributed images a LMMSE approachrdquo IEEE Transactionson Image Processing vol 17 no 8 pp 1383ndash1398 2008

[36] H Gudbjartsson and S Patz ldquoe Rician distribution of noisyMRI datardquo Magnetic Resonance in Medicine vol 34 no 6pp 910ndash914 1995

[37] R W Liu L Shi W Huang et al ldquoGeneralized total vari-ation-based MRI Rician denoising model with spatiallyadaptive regularization parametersrdquo Magnetic ResonanceImaging vol 32 no 6 pp 702ndash720 2014

[38] M Xu J Alirezaie and P Babyn ldquoLow-dose CT denoisingwith dilated residual networkrdquo in Proceedings of the 2018 40thAnnual International Conference of the IEEE Engineering inMedicine and Biology Society (EMBC) pp 5117ndash5120 Hon-olulu HI USA July 2018

[39] F Yu and V Koltun ldquoMulti-scale context aggregation bydilated convolutionsrdquo 2015 httpsarxivorgabs151107122

[40] Y Peng L Zhang S Liu X Wu Y Zhang and X WangldquoDilated residual networks with symmetric skip connectionfor image denoisingrdquo Neurocomputing vol 345 pp 67ndash762019

[41] X Zhang W Yang Y Hu et al ldquoDMCNN Dual-domainmulti-scale convolutional neural network for compressionartifacts removalrdquo in Proceedings of the 2018 25th IEEE In-ternational Conference on Image Processing (ICIP) pp 390ndash394 Athens Greece October 2018

[42] F Chollet ldquoXception deep learning with depthwise separableconvolutionsrdquo in Proceedings of the 2017 IEEE Conference onComputer Vision and Pattern Recognition (CVPR)pp 1800ndash1807 Honolulu HI USA July 2017

[43] A G Howard M Zhu B Chen et al ldquoMobilenets efficientconvolutional neural networks for mobile vision applica-tionsrdquo 2017 httpsarxivorgabs170404861

[44] M Sandler A Howard M Zhu et al ldquoMobilenetv2 invertedresiduals and linear bottlenecksrdquo in Proceedings of the 2018IEEECVF Conference on Computer Vision and Pattern Rec-ognition pp 4510ndash4520 Salt Lake City UT USA June 2018

[45] S Angizi Z He A S Rakin et al ldquoCMP-PIM an energy-efficient comparator-based processing-in-memory neuralnetwork acceleratorrdquo in Proceedings of the 2018 55th ACMESDAIEEE Design Automation Conference (DAC) pp 1ndash6San Francisco CA USA June 2018

[46] R Imamura T Itasaka and M Okuda ldquoZero-Shot Hyper-spectral Image Denoising with Separable Image Priorrdquo inProceedings of the 2019 IEEECVF International Conference onComputer Vision Workshop (ICCVW) pp 1416ndash1420 SeoulSouth Korea October 2019

[47] L-C Chen G Papandreou I Kokkinos K Murphy andA L Yuille ldquoDeepLab semantic image segmentation withdeep convolutional nets atrous convolution and fully con-nected CRFsrdquo IEEE Transactions on Pattern Analysis andMachine Intelligence vol 40 no 4 pp 834ndash848 2018


[48] C A Cocosco V Kollokian R K S Kwan et al ldquoBrainwebonline interface to a 3D MRI simulated brain databaserdquoNeuroImage vol 5 p 425 1997

[49] R K-S Kwan A C Evans and G B Pike ldquoAn extensibleMRI simulator for post-processing evaluationrdquo in LectureNotes in Computer Science pp 135ndash140 Springer BerlinGermany 1996

[50] C D Constantinides E Atalar and E R McVeigh ldquoSignal-to-noise measurements in magnitude images from NMRphased arraysrdquo Magnetic Resonance in Medicine vol 38no 5 pp 852ndash857 1997

[51] A Hammers C-H Chen L Lemieux et al ldquoStatisticalneuroanatomy of the human inferior frontal gyrus andprobabilistic atlas in a standard stereotaxic spacerdquo HumanBrain Mapping vol 28 no 1 pp 34ndash48 2007

[52] J V Allom and P Coupe ldquovolBrain an online MRI brainvolumetry systemrdquo Frontiers in Neuroinformatics vol 10no 54 pp 1ndash14 2016

[53] C R Jack and Jr Alzheimerrsquos disease neuroimaging initiativedataset httpadniloniuscedu

[54] A Foi ldquoNoise estimation and removal in MR imaging thevariance-stabilization approachrdquo in Proceedings of the 2011IEEE International Symposium on Biomedical Imaging FromNano toMacro pp 1809ndash1814 Chicago IL USAMarch 2011

[55] A E Kavur N S Gezer M Barıs et al ldquoCHAOS Challenge -combined (CT-MR) healthy abdominal organ segmentationrdquoMedical Image Analysis vol 69 Article ID 101950 2021

[56] A E Aslan M A Selver O Dicle M Barıs and N S GezerldquoCHAOSmdashCombined (CT-MR) Healthy Abdominal OrganSegmentation Challenge Datardquo 2019

[57] J V Manjon P Coupe A Buades et al ldquoNew methods forMRI denoising based on sparseness and self-similarityrdquoMedical Image Analysis vol 16 no 1 pp 18ndash27 2012

[58] S Louis Collins K R L Reddy and D S Rao ldquoDenoising andsegmentation of MR images using fourth order non-linearadaptive PDE and new convergent clusteringrdquo InternationalJournal of Imaging Systems and Technology vol 29 no 3pp 195ndash209 2019

[59] O Oktay E Ferrante K Kamnitsas et al ldquoAnatomicallyconstrained neural networks (ACNNs) application to cardiacimage enhancement and segmentationrdquo IEEE Transactions onMedical Imaging vol 37 no 2 pp 384ndash395 2018

[60] Y Heinrich B Zhang W Zhao et al ldquoMagnetic resonanceimage denoising algorithm based on cartoon texture andresidual partsrdquo Computational and Mathematical Methods inMedicine vol 2020 Article ID 1405647 10 pages 2020


method and verified it on diffusion-weighted MR images[10] Satheesh et al developed an MR image denoising al-gorithm using the contourlet transform which achieved ahigher peak signal-to-noise ratio than the wavelet transform[11] Zhang et al used an improved singular value de-composition method to denoise simulated and real 3Dimages e experimental results showed that their methodwas superior to the existing denoising methods [12] Lealet al presented a method based on sparse representationsand singular value decomposition (SVD) for nonlocallydenoising MR images is method prevents blurring ar-tifacts and residual noise [13] In addition by extending thelocal region to a nonlocal scheme the nonlocal means(NLM) strategy was used for MR image denoising [14ndash16]Gautam et al proposed a novel denoising technique for MRimages based on the advanced NLM method with non-subsampled shearlet transform (NSST) [17] Kanoun et alproposed an enhanced NLM filter using the Kolmogorov-Smirnov (KS) distance e experimental results providedexcellent noise reduction and image-detail preservation [18]

In recent years the explosive development of deeplearning has suggested a new methodology for imagedenoising It can use multiple convolution filters to auto-matically extract features with large receptive fields toreconstruct high-resolution images In [19] the authors usedthe self-encoder to train the image features of differentresolutions to achieve adaptive denoising Zhang et alexploited denoising convolutional neural networks(DnCNNs) for Gaussian noise removal and achieved ex-cellent performance by using residual learning strategy [20]Cherukuri et al applied a deep learning network that lev-eraged the prior spatial structure of images to reconstructhigh-resolution images [21] Manjoprimen et al proposed a novelautomatic MR image denoising method by combining aconvolutional neural network (CNN) with a traditional filter[22]

Deep learning-based denoising methods can graspricher contextual information in large regions to improveperformance With very deep architectures it can expandthe receptive field of the network to capture more globalcontextual information over large image regions Liu et alutilized the multiscale fusion convolution network(MFCN) to perform super-resolution reconstruction ofMR images [23] Pham et al used a deep 3D CNN modelwith residual learning to reconstruct MR images [24] eirmodel exploited a very deep architecture with a large re-ceptive field to acquire a powerful learning ability Jianget al described a multichannel denoising convolutionalneural network (MCDnCNN) that directly learned theprocess of denoising and performed experiments onsimulation and real MR data [25] In [26] Ran et alsuggested a residual encoder-decoder Wasserstein gener-ated countermeasure network (RED-WGAN) for MRimage denoising Hong et al designed a spatial attentionmechanism to obtain the area of interest in MR imageswhich made use of the multilevel structure and boosted theexpressive ability of the network [27] Tripathi and Bagproposed a novel CNN for MR image denoising eproposed model consisted of multiple convolutions that

captured different image features while separating inherentnoise [28] Li et al designed a progressive network learningstrategy by fitting the distribution of pixel-level and fea-ture-level intensities eir experimental results demon-strated the great potential of the proposed network [29]Gregory et al created HydraNet a multibranch deep neuralnetwork architecture that learned to denoise MR images ata multitude of noise levels and proved the superiority ofthe network on denoising complex noise distributionscompared to some deep learning-based methods [30]Aetesam and Maji proposed a neural framework for MRimages denoising using an ensemble-based residuallearning strategy High metric value and high-quality visualresults were obtained in both synthetic and real noisydatasets [31]

In the above reported deep learning denoising tasks thedepth and width of the networks were often increased tocapture more contextual information However thesemethods introduced a number of parameters which made itdifficult to train the denoising models Some of the methodslearned the Rician noise distribution solely by stackingconvolution layers which easily overlooked much localinformation and led to unsatisfactory denoising results atsome key local anatomical positions

To address the above shortcomings this work proposesa novel network termed 3D-Parallel-RicianNet that is usedto remove the noise of MR images First to expand thereceptive field without introducing more parameters wedesign a dilated convolution residual (DCR) module anduse it to build a subnetwork (DCRNet) that can extractglobal information by cascading en a depthwise sepa-rable convolution residual (DSCR) module is designed andused to construct a subnetwork (DSCRNet) to extract localinformation Finally the features of each module ofDCRNet and DSCRNet are merged and cascaded to obtainfull-scale mappings between image appearances and noisedeviation

e main contributions of this work are summarized asfollows

(1) DCRNet expands the receptive field to extract richcontext information through cascading DCR mod-ules which capture the real Rician distribution in theglobal area

(2) DSCRNet uses the DSCR module to focus on thelocal area of the image and effectively removes localanatomical noise Each DSCR module of this sub-network is added to the output part of each DCRmodule of the corresponding DCRNet

(3) e 3D-Parallel-RicianNet uses a residual learningmechanism to prevent vanishing and explodinggradient problems

e remainder of this work is organized as follows InSection 2 we describe the proposed denoising networksand loss function en in Section 3 we present theexperimental tests of our approach on synthetic and realMR noisy data Additionally a comparison of our methodwith state-of-the-art algorithms is provided Finally in





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MethodCSF GM WM



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35 Clinical Results




























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MethodCSF GM WM



R 1 R 2 R 3PSNR 410253 404788 393627SSIM 09956 09661 09946





Data Availability




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35 Clinical Results




























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MethodCSF GM WM



R 1 R 2 R 3PSNR 410253 404788 393627SSIM 09956 09661 09946





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Acknowledgments



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MethodCSF GM WM



R 1 R 2 R 3PSNR 410253 404788 393627SSIM 09956 09661 09946





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35 Clinical Results




























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35 Clinical Results




























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MethodCSF GM WM



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MethodCSF GM WM



R 1 R 2 R 3PSNR 410253 404788 393627SSIM 09956 09661 09946





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SSIM








(a) (b) (c) (d) (e) (f )

(g) (h) (i) (j) (k)


(a) (b) (c) (d) (e) (f )

(g) (h) (i) (j) (k) (l)



(a) (b) (c)

(d) (e) (f )


18

17

16

15

14En

tropy

NLM

BM3D

OD

CT3D

PRI-

NLM

3D

CNN

-DM

RI

Rici

anN

et

2D-D

CRN

et

2D-P

aral

lel-R

icia

nNet

3D-D

CRN

et

3D-P

aral

lel-R

icia

nNet

Noi

sy im

age















MethodCSF GM WM



R 1 R 2 R 3PSNR 410253 404788 393627SSIM 09956 09661 09946





Data Availability




Acknowledgments



References

































































1 3 5 7 920

25

30

35

40

45

50

PSN

R (d

B)

Noise level ()




(a) (b) (c) (d) (e) (f)

(g) (h) (i) (j) (k) (l)








0

1

2

3

4

5

Entr

opy


1 3 5 7 9

080

085

090

095

100

Noise level ()

SSIM








(a) (b) (c) (d) (e) (f )

(g) (h) (i) (j) (k)


(a) (b) (c) (d) (e) (f )

(g) (h) (i) (j) (k) (l)



(a) (b) (c)

(d) (e) (f )


18

17

16

15

14En

tropy

NLM

BM3D

OD

CT3D

PRI-

NLM

3D

CNN

-DM

RI

Rici

anN

et

2D-D

CRN

et

2D-P

aral

lel-R

icia

nNet

3D-D

CRN

et

3D-P

aral

lel-R

icia

nNet

Noi

sy im

age















MethodCSF GM WM



R 1 R 2 R 3PSNR 410253 404788 393627SSIM 09956 09661 09946





Data Availability




Acknowledgments



References






































































0

1

2

3

4

5

Entr

opy


1 3 5 7 9

080

085

090

095

100

Noise level ()

SSIM








(a) (b) (c) (d) (e) (f )

(g) (h) (i) (j) (k)


(a) (b) (c) (d) (e) (f )

(g) (h) (i) (j) (k) (l)



(a) (b) (c)

(d) (e) (f )


18

17

16

15

14En

tropy

NLM

BM3D

OD

CT3D

PRI-

NLM

3D

CNN

-DM

RI

Rici

anN

et

2D-D

CRN

et

2D-P

aral

lel-R

icia

nNet

3D-D

CRN

et

3D-P

aral

lel-R

icia

nNet

Noi

sy im

age















MethodCSF GM WM



R 1 R 2 R 3PSNR 410253 404788 393627SSIM 09956 09661 09946





Data Availability




Acknowledgments



References




































































(a) (b) (c) (d) (e) (f )

(g) (h) (i) (j) (k)


(a) (b) (c) (d) (e) (f )

(g) (h) (i) (j) (k) (l)



(a) (b) (c)

(d) (e) (f )


18

17

16

15

14En

tropy

NLM

BM3D

OD

CT3D

PRI-

NLM

3D

CNN

-DM

RI

Rici

anN

et

2D-D

CRN

et

2D-P

aral

lel-R

icia

nNet

3D-D

CRN

et

3D-P

aral

lel-R

icia

nNet

Noi

sy im

age















MethodCSF GM WM



R 1 R 2 R 3PSNR 410253 404788 393627SSIM 09956 09661 09946





Data Availability




Acknowledgments



References

































































(a) (b) (c)

(d) (e) (f )


18

17

16

15

14En

tropy

NLM

BM3D

OD

CT3D

PRI-

NLM

3D

CNN

-DM

RI

Rici

anN

et

2D-D

CRN

et

2D-P

aral

lel-R

icia

nNet

3D-D

CRN

et

3D-P

aral

lel-R

icia

nNet

Noi

sy im

age















MethodCSF GM WM



R 1 R 2 R 3PSNR 410253 404788 393627SSIM 09956 09661 09946





Data Availability




Acknowledgments



References











































































MethodCSF GM WM



R 1 R 2 R 3PSNR 410253 404788 393627SSIM 09956 09661 09946





Data Availability




Acknowledgments



References




































































Data Availability




Acknowledgments



References

































































Denoisingof3DBrainMRImageswithParallelResidual ...Parallel-RicianNet, which will combine global and...

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Transcript of Denoisingof3DBrainMRImageswithParallelResidual ...Parallel-RicianNet, which will combine global and...