Accelerated 4D flow MRIComparing SENSE, k-t PCA and Compressed Sensing

Tomas Kaandorp10356169

Patient comfort can be increased by accelerating an MRI scanner toreduce scan time. 4D flow MRI scans can be accelerated by

undersampling the k-space. Unfortunately this has a negative effect onthe image quality and signal-to-noise ratio. To look at the effects of

undersampling on the flow amplitude, SENSE, k-t PCA and CompressedSensing (CS) are compared for acceleration factors (R): 6, 8, and 10 in

five healthy volunteers. The results show that the maximum flowamplitude decreases for all scanning modalities if R increases . The

average drop in flow amplitude for SENSE, k-t PCA and CS arerespectively: 33 %, 20 %, and 7.5 %. Furthermore CS showed a better

image quality for higher R compared to SENSE and k-t PCA, which leadsto reliable flow curves and usable image quality up to R10. Thus CS

shows promising results for reliable shortening of 4D flow MRI in clinicalenvironments.

Report Bachelor Project Physics and Astronomy, size 15 EC, conductedbetween 01-04–2017 and 01-08–2017

Supervisor: Dr. Ir. A. J. NederveenSecond assessor: Prof. Dr. Ir. G. J. Strijkers

Mentor: L. M. Gottwald

Department of Radiology and Nucleair medicineAmsterdam Medical CentreUniversity of Amsterdam

August 2017

Contents

1 Introduction 2

2 Theory 22.1 MRI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22.2 Acceleration methods . . . . . . . . . . . . . . . . . . . . . . . . 32.3 Hypothesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

3 Method 73.1 Phantom scan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73.2 In vivo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83.3 SNR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

4 Results 84.1 Phantom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84.2 In vivo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104.3 Prospective vs retrospective triggering . . . . . . . . . . . . . . . 164.4 SNR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

5 Discussion 19

6 Conclusion 20

7 References 21

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1 Introduction

The global average life expectancy has tremendously increased for decades. Thismeans that the number of people dying from cardiovascular diseases (CV) is onthe rise, and is now even the primary cause of premature deaths (Heissel, 2017).For the correct diagnosis and treatment a 4D flow MRI scan might be beneficial.For example, a 4D flow MRI scan allows physicians to look at blood flow, peakblood flow and wall shear stress. However these scans needed for the diagnosisare high resolution scans which means they take a long time. This in term meansthat patients have to lie inside the scanner for a prolonged period of time, whichcan be claustrophobic or uncomfortable. To increase patient well-being it is vitalto reduce scanning time of 4D flow MRI. However accelerating an MRI scan hasa negative trade-off to the image quality of the scan, this trade-off is expressedin terms of the Signal-to-Noise Ratio (SNR). It is therefor vital to finding a wayto shorten the scan time without the drop in image quality.

Over the years the scan time of 4D flow has been shortened i.e. by threemethods. First by the implementation of multiple receiving coils (Pruessmannet. al., 1999), secondly by the use of k-t Principal Component Analyses (k-tPCA) and more recently by implementing Compressed Sensing (CS). Since theaorta is of interest to diagnose CV, this paper will compare the aorta bloodflow for SENSE, k-t PCA and CS to see if the acceleration has an effect on thereliability of the blood flow quantization.

2 Theory

2.1 MRI

A MRI scanner uses the 1H spin of the Nucleus to acquire an image. Firstlya subject (i.e. volunteer or patient) is placed into a homogeneous magneticfield (the scanner). By doing so, all the nuclear spins of the atoms align into the foot head direction. Once all the spins are aligned, a Radio Frequency(RF) pulse is given with a frequency matching the Larmor frequency of 1H.This RF-pulse makes the nuclear spin resonate. When resonating the spinssend out a RF signal which can be measured with the receiving coil. This canbe done via T1 imaging of T2 imaging, depending on what sort of tissue thatis scanned. The difference is determined by the time the 1H nucleus remainsresonating. To transfer the frequencies measured during acquisition a Fouriertransform is used. The frequencies are measured in the Frequency space, alsocalled k-space. In principle the entire k-space needs to be scanned to get agood image quality. If only parts of the k-space are scanned the image becomesblurry and other artifacts appear. Over the years a number of methods wheredevised to scan the k-space. Initially k-space was scanned in horizontal row (kxdirection) progressing downwards in the vertical direction (ky) after scanningeach horizontal row.

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Figure 1: The Nyquist criterion sets the required k-space coverage, which canbe achieved using various sampling trajectories. Image resolution is determinedby the extent of the k-space coverage. The supported field of view is determinedby the sampling density. Violation of the Nyquist criterion causes artifacts inlinear reconstructions, which depend on the sampling pattern. (Lustig et. al.,2008)

Although there are multiple ways of scanning the k-space a Cartesian grid ispreferred since this can be easily transformed from frequency domain to spacedomain by a Fourier transform. New techniques such as spiral trajectories basedon radial coordinates are gaining popularity since these are less susceptible tomotion artifacts and can be more easily under-sampled than Cartesian trajec-tories (Lustig et. al., 2008).

2.2 Acceleration methods

Accelerating MRI scans is mainly done by collecting less data points. Data iscollected in the frequency domain (k-space). By collecting less data points inthe k-space, i.e. under sampling the k-space, the duration of the scan shortens.However this is where a trade off arises. A fully sampled k-space is neededfor high resolution images which physicians like, but this takes time. Undersampling the k-space shortens the scan time but this also means the imagequality of the scan deteriorates. This trade off is expressed in the Signal-to-Noise Ratio (Formula 1)

SNR =Signalintensity

SD(Noiseintensity)(1)

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In short, if a scan is accelerated, the SNR decreases which means the imagequality decreases.

One way of accelerating MRI scans is by using a SENSE reconstruction. Duringa SENSE scan, data is collected using multiple receiver coils. This means thereare multiple images created (i. e. 2). These images contain aliasing effects sincethey are based on only part of the k-space. By later combining these multipleimages, one complete image is created and aliasing effects are minimized. Thishowever requires the scanner to save all the images during the scan and to forma reconstructed image by superposition of these saved images weighted by thecorresponding coil sensitivity maps.

Figure 2: SENSE graphically displayed, two images with aliasing formed bydifferent coils. Afterwards these images are combined using a superpositionweighted by coil sensitivity maps (MRIquestions.com, 2017)

Another way of reducing scan time is by under sampling the k-space overtime, this method is called k-t PCA. Next an adaptive filter is used in theFourier transformed domain to correct for the aliasing effects that occur due tothe under sampling. However, the reconstruction is now under determined sincethe filter leads to more unknown values than equations. This has a negative ef-fect on the temporal fidelity. To solve this problem k-t BLAST is revised to k-tPCA. Principle Component Analysis (PCA) reduces a multi-dimensional dataset to a lower dimensional set by using a training image. PCA constrains theappearance of the object such that the frequency must be a linear combinationof predefined basis functions. The basis functions are derived from the trainingimage. The PCA reconstruction separates the overlapped images accurately.Since the temporal fidelity is also separated, there is no negative effect on thefidelity. Therefore, k-t PCA then leads to a shorter 4D flow scan time. Unfor-tunately this still leads to some aliasing in the image. This means the imagequality decreases and it may become difficult to define a correct Region Of In-terest (ROI). Thus, limiting the acceleration factor (R). Gwenael Page et. al.,

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2017 showed that it is possible to accelerate the scan using R = 8 and retain agood image quality. However the flow amplitude decreases significantly aboveR6. Thus limiting 4D flow MRI.

Figure 3: An example of k-t PCA. Firstly the training image is made (a), thenthe data is under sampled (b). By using a filter to correct for the aliasing effect,the image becomes under determined which is solved with the training image(c).(Petersen et. al., 2009)

A more recent development is called Compressed Sensing (CS). CS also undersamples the k-space but has some more requirements. Firstly the data has tobe under sampled in a random way. Secondly, transform sparsity is needed andlastly, to acquire the best image quality, an iterative reconstruction method isneeded.

There are again a number of ways to scan the k-space, a Poisson distributionin Cartesian coordinates can be used. However a spiral shape with more datapoints in the centre than on the outer radius shows promising results in scantime reduction and image quality(L. M. Gottwald et. al., 2017).

The collected data has to be incoherent/sparse to make it possible to separatenoise from the signal. Via a wavelet transform, the data is made sparse which isnecessary to do the further data analyses. In the sparse data set, the strongestsignal is identified and abstracted from the whole signal. In the next iteration ofdata process, the signal then allows for the identification of a signal with a lowerintensity. After multiple iterations only the noise remains and the completespectrum of signals is identified. In Figure 2, the CS reconstruction is graphically

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displayed. After the separation of the signals, the image can be reconstructedthrough the regular methods i.e. a Fast Fourier transform(FFT). Because allsignals are deduced from the under sampled k-space, the image quality remainsacceptable for clinical use (Lustig et. al., 2008).

Figure 4: Heuristic procedure for reconstruction from under sampled data. Asparse signal (a) is 8-fold under sampled in its 1-D k-space domain (b). Equi-spaced under sampling results in signal aliasing (d) preventing recovery. Pseudo-random under sampling results in incoherent interference (c). Some strongsignal components stick above the interference level, are detected and recoveredby thresholding (e) and (f). The interference of these components is computed(g) and subtracted (h), thus lowering the total interference level and enablingrecovery of weaker components.(Lustig et. al., 2008

2.3 Hypothesis

Based on the paper from Gwenael Page et. al., 2017, it is expected that forSENSE and k-t PCA the amplitude of the flow curves decrease if the accelerationfactor (R) is higher then R6.

Secondly, since the SNR decreases if the acceleration rate increases, it is tobe expected that the image quality decreases. Since this effect is greater forSENSE than for k-t PCA or CS, it is expected that SENSE has the worst imagequality and thus lowest SNR, followed by k-t PCA. Since the CS reconstructionis better in determining the signals with low intensity because it uses an iterativereconstruction method, CS should have a better image quality. Therefore theaverage SNR of CS should be higher than the average SNR of k-t PCA andSENSE.

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3 Method

3.1 Phantom scan

Firstly, an exploratory scan was made with a carotid bifurcation phantom(LifeTec, Eindhoven, Netherlands). A pulsating water flow with a simulatedheart rate of 60 bpm and a variability of 5 bpm created a temporal mean flowof 300 ml/min. A time stamp from the pump signal was used for retrospectivetriggering. A schematic overview of the experimental setup and all measurementparameters are shown in Figure 5.

Figure 5: Experimental setup used for the Phantom scans, (L. M. Gottwald,2017)

All experiments were conducted on a 3T MRI scanner (Philips Healthcare,Best, Netherlands) using an 8-channel neck coil. A total matrix size(FOV)of 64x64x64 mm3 and a voxel size of 1x1x1 mm3 was acquired in three flowencoding directions using a VENC of 150 cm/s. Profile lists of different lengthswere created with a nominal acceleration factor (R) of 2, 4, 6, 8 and 10 peracceleration method i.e. SENSE and k-t PCA. The acquired data was processedby ReconFrame (Gyrotools, Zurich, Zwiterland) and retrospectively absolutebinned in 24 cardiac frames.

For the flow analysis the return artery was used since this was the largestphantom artery and thus yields the highest signal. Next Matlab(The Math-Works Inc, r2016b) was used to draw Regions Of Interest (ROI). Based onthese ROI, a Black and White (BW) mask was created. This BW mask wasthen used to make the flow curves since it multiplies the data in the aorta with1 and all other areas with 0. The flow curves are compared to the pre-set max-imum flow and pulsation of the phantom. The flow was quantified using thePhase image. The phase data was multiplied with the BW mask so only theAorta was selected. Next the flow data was scaled to the voxel size and thepreset VENC. This was done using Formula 2 and 3.

V elocityROI = mean(BWmask ×Dataset) (2)

AverageF lowROI = mean(V elocityROI ×BWArea

100) (3)

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3.2 In vivo

Secondly the flow was compared in vivo. This was also done on a 3T MRIscanner (Phillips Healthcare, Best, Netherlands) using a 16-channel Torso andan 8-channel posterior coil. Five healthy volunteers, aged between 20-25 yearswhere scanned. A total FOV size of 315x275x60 mm3 and a VENC of 150 cm/swas used, the resolution was set to 2.5x2.5x2.5 mm3. Data was collected inthree different flow encoding directions for each acceleration method(SENSE,k-t PCA and CS). Scanning R2 and R4 would lead to a longer scanning timethen 1.5 hours. It becomes very uncomfortable for a volunteer to lay insidethe scanner longer then 1.5 hours, therefor R2 and R4 are not included in thispaper.

The ROI was drawn on the Ascending Aorta (AAO) for all 24 cardiac frames.next this was scaled for the phase offset. To calculate the flow Equation 2 and3 where used again. Next the mean flow is determined over all volunteers. Theflow curves are compared based on the acceleration rate (R) with fixed modalityand also compared per modality with fixed R.

Furthermore it was investigated if retrospective cardiac synchronization dif-fers from prospective cardiac synchronization. This is done by comparing data,for a fixed R, between retrospective and prospective gating for CS and k-t PCA.This can be interesting since it may occur that data is not binned correctly inretrospective binning than with prospective binning (triggering).

3.3 SNR

Lastly, the SNR is compared. This is done by making two extra ROI. The firstone is inside the body but on a location where there should be no significantchange in the signal intensity. The second ROI is then drawn outside the bodywhere only noise is expected. By using Formula 1 the SNR is calculated. Incontrary to the flow, the SNR is calculated based on the magnitude image andnot on the phase image. This is done since the intensity in a phase image canchange around the blood vessels due to blood flow.

4 Results

4.1 Phantom

Firstly, a Phantom was examined for k-t PCA and SENSE, the flow curves peracceleration rate are displayed in Figure 6. As Page et. al., 2017, predicted,the amplitude of the flow curves declines as the acceleration rate (R) increases.Furthermore it can be seen that the lines become less smooth for increased R.Both these observations are due to the undersampling of the data.

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Figure 6: Flow comparison in the Phantom, expressed for fixed R. Notice thedrop in maximum flow amplitude.

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4.2 In vivo

First the image quality of the magnitude images are compared to see if the datais usable and how the undersampling effects the image quality. This comparisonis done by eye based on Figure 7

Figure 7: on the x-axis R 6, 8, and 10 are displayed. On the y-axis CS, k-tPCA and Sense are displayed. On the top row it is visible that SENSE is verynoisy and unclear. Below kt-pca shows a good image quality for all R althoughsome streaking appears. On the bottom CS also shows good image quality. Theimage is a bit blurry due to scaling. CS is scaled by multiplying with 0.2 andSENSE by multiplying with 2

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During the drawing of the ROI it became clear that the aorta was verydifficult to locate on the accelerated SENSE scans. Since the volunteers wherescanned for multiple scanning modalities, sometimes k-t PCA or CS scans whereused to draw the ROI.

Firstly, the differences in the flow curves is compared within each scanningmodality, in Figure 8 the flow for all R is plotted for SENSE.

Figure 8: Mean flow for SENSE. R 6, 8, and 10 are compared. R6 shows noreal flow. This may be due to a small and incorrect data set. The max flowamplitude of R10 is lower then R8.

It can be seen that the flow curves are very rough, also R6 preforms verybad compared to R8 and R10. This might be because the mean R6 flow isdetermined on less than five volunteers due to some failed scans. The decreasein amplitude between R8 and R10 is neatly visible.

In Figure 9, k-t PCA is compared between acceleration rate (R). The flowcurves preform better and are smoother compared to SENSE. Again the dropin amplitude is visible as predicted by Page et. al. On the x-axis the cardiacframes are displayed. In all flow curves we can see when the heart makes a beat.First a peak is visible since the heart is pumping, next the a slow relaxationoccurs. During the relaxation some low peaks are still caused by the relaxation

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of the slightly expanded aorta due to the blood pressure. On the y-axis, theMean blood flow is given in ml/s.

Figure 9: Mean flow for k-t PCA. R 6, 8, and 10 are compared. The drop inamplitude is visible and for low R the graphs are smoother due to less under-sampling.

Figure 10 shows the mean flow curves of CS. Here it can be seen that themax amplitude is almost constant. Again as expected the amplitude does drop,the difference between the highest peak (R6) and the lowest peak (R8) is 14.75ml/s. The amplitude difference between R8 and R10 can not be calculated dueto a difference in cardiac frames. However since the peak flow amplitude of R10lies between the peak flow of R8 and R6 this is still smaller then 14.75 ml/s.

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Figure 10: Mean flow for CS. R 6, 8, and 10 are compared. The difference inmax flow between R8 and R6 is 14.75 ml/s

Next the differences per modality are compared.

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Figure 11: Mean flow for SENSE, k-t PCA, and CS for R6

Figure 12: Mean flow for SENSE, k-t PCA, and CS for R8

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Figure 13: Mean flow for SENSE, k-t PCA, and CS for R10.

Again CS preforms stable with a maximum flow around 160 ml/s SENSEpreforms well for R8 but decreases signifcantly compared to CS for R10. Fork-t PCA a steady drop can be seen in maximum amplitude for all R comparedto SENSE and CS. Also the curve remains reasonably smooth. The maximumdifference in flow amplitude between R6 and R10 for SENSE, k-t PCA and CSare respectively: 33%, 20%, and 7.5%.

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4.3 Prospective vs retrospective triggering

It can be seen in Figures 14, 15, 16, and 17 that retrospective binning leadsto a binning error at the end of the flow curves. A ascending line can be seenwhich should actually be at the beginning of the flow curve. Furthermore itcan be seen that the amplitude for retrospective binning matches more to theamplitude of CS and SENSE.

Figure 14: Mean flow for retrospective and prospective binning in the AAoaccelerated to R8. A small binning error can be seen at the end of the flowcurve for retrospective binning.

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Figure 15: Velocity for retrospective and prospective binning in the AAo accel-erated to R8. A small binning error can be seen at the end of the flow curve forretrospective binning.

Figure 16: Mean flow for retrospective and prospective binning in the DAoaccelerated to R8. A small binning error can be seen at the end of the flowcurve for retrospective binning.

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Figure 17: Velocity for retrospective and prospective binning in the DAo accel-erated to R8. A small binning error can be seen at the end of the flow curve forretrospective binning.

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4.4 SNR

As the acceleration rate (R) increases, the increased under sampling of the k-space leads to a decrease in signal intensity. Therefor, the SNR calculated withFormula 1 should drop. Since the image quality for CS is also better then forSENSE or k-t PCA, it is also expected that the SNR is higher for CS than forSENSE and k-t PCA. However this is not what is seen in the data. The SNRvalues are given below in Table 1.

SENSE k-t PCA CSR6 3.45 3.39 48.17R8 4.09 4.09 54.15R10 2.67 2.62 58.70

Tabel 1: average SNR expressed per method and R

As seen in the table, CS has an higher average SNR than k-t PCA or SENSEover all volunteers. Furthermore there is an unexpected peak in the average SNRfor R8 in SENSE and k-t PCA. As expected the SNR value for R10 are belowR6 for k-t PCA and SENSE as should be based on the fact that the signaldecreases if the undersampling increases.

5 Discussion

Not all scans could be performed one after the other due to a software changeduring the examination, resulting in a scan break. Moreover, some exams hadto be spitted into two exams, when the gating efficiency of the subject had beenvery poor. The composition of the subject scans and masks are shown in Table2.

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Volunteer: 1 2 3 4 5Mask 1 SENSE + kt-PCA 4 SENSE + k-t PCA SENSE 2.45 + k-t PCA SENSE + k-t PCA Kt-PCAMask 2 CS CS CS + SENSE 2.8, 3.2 CS CS + SENSEMask 3 k-t PCA: 6, 8

Table 2: Composition of scanned volunteer and corresponding BW masks

The drawing of the ROI remains a human task. This means it is susceptibleto flaws such as drawing the ROI to big or to small. Drawing the ROI wrongcan lead to misguided flow curves. One other solution is to only look at thevelocity since this is not scaled for the area of the ROI.

Furthermore, in determining the Signal-to-Noise Ratio (SNR), it was as-sumed that the signal outside of the body would only contain noise. It may bepossible that the signal outside the body is also scaled depending on the scanmodality used. Thus the used baseline of noise would differ per modality and itwould not be able to make a good comparison.

The average SNR for CS is about 20 times higher than the SNR for SENSEand k-t PCA. This might be explained by a scaling factor. There are alsostrong indications that the SNR is influenced by the multiple scanning sessionsof volunteers and the software update of the scanner. For example the CS SNRfor volunteer two is around 17 while all the other SNR are around 50. Volunteertwo was scanned with CS before the scanner update whilst all other volunteerswhere scanned with CS after the scanner update. Therefore it is clear thescanner update has influenced either the scaling of the reconstruction method.

6 Conclusion

Just like Page Et. Al. showed, the amplitude of the flow curves drops for allmodalities if the acceleration rate increases. However the drop in flow amplitudefor CS is limited to 14.75 ml/s between R6 and R8. Since R10 lies between R6and R8 the difference of 14.75 ml/s is a maximum difference.

The image quality does decrease if R increases. For SENSE the decrease inimage quality means that it is no longer possible to draw the correct ROI. For k-tPCA the image quality remains acceptable but the max flow amplitude decreasessignificantly. For CS the image quality also remains acceptable and the decreasein max flow amplitude is limited to 14.75 ml/s up to R = 10. This is roughly7 % of the maximum flow for R6 whilst the drop in amplitude for SENSE andk-t PCA are respectively 33% and 20%. Therefore CS shows promising resultsfor reliably shortening the scan time of a 4D flow MRI. However there are stillother limiting factors such as the gating efficiency. It is advisable to do somefurther research into 4d flow MRI but also into the gating efficiency.

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7 References

Heiddel W, Deaths from cardiovasculair disease increase globally while mortal-ity rates decrease, Healthdata, www.healthdata.com, 2017, retrieved 17-08-2017.

Gottwald L. M, Peper E. S, Zang Q, Pronk V, Coolen B. F, Strijkers G. J,Nederveen A. J, Compressed Sensing accelerated 4D flow MRI using a pseudospiral Cartesian sampling technique with random undersamling in time, Un-known, 2017

Lustig M, Donoh D, Santos J, Compressed sensing MRI, IEEE SIGNALPROCESSING MAGAZINE,] MARCH 2008, 72-82.

MRI questions, retrieved 17-08-2017. www.mriquestions.com/senseasset

Page G, Bettoni J, Salsac A.V, Baledent O, Influence of the k-t PrincipalComponent Analysis acceleration factor on the accuracy of flow measurementin 4D PC-MRI, Proc. Intl. Soc. Mag. Reson. Med. 25 (2017)

Pedersen H, Kozerke S, Ringgaard S, Nehrke K, and Kim W, k-t PCA:Temporally Constrained k-t BLAST Reconstruction Using Principal Compo-nent Analysis, Magnetic Resonance in Medicine, 2009, 62, 706-716.

Pruessmann K. P, Weiger M, Scheidegger M. B, Boesiger P, SENSE: Sen-sitivity Encoding for Fast MRI, Magnetic Resonance in Medicine, 1999, 42,952-962.

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