Sherman Braganza , Miriam Leeser, W.C. Warger II, C.M. Warner, C. A. DiMarzio [email protected]...
1
Sherman Braganza , Miriam Leeser, W.C. Warger II, C.M. Warner, C. A. DiMarzio [email protected] [email protected] Goal Accelerate the performance of the minimum L P Norm phase unwrapping algorithm using Field Programmable Gate Arrays (FPGAs) Abstract Over the past several years, the development of coherent imaging techniques has increased dramatically and now applications such as Magnetic Resonance Imaging (MRI) and Synthetic Aperture Radar(SAR) are commonplace. At Northeastern University, a coherent imaging process known as Optical Quadrature Microscopy (OQM) has been developed for the purpose of non- invasively capturing the amplitude and phase data of an optically transparent sample. This can be used to reconstruct images of the original sample. However, sensors and basic signal processing produce a non-linearly wrapped phase lying in the range of (-,]. In the presence of noise, the unwrapping of the phase data can fail catastrophically. Robust methods have been proposed that unwrap around noisy sections thus preserving as much data as possible. Other methods that minimize noise through numerical error minimization techniques are also commonly used. We aim to implement a phase unwrapping algorithm on reconfigurable hardware. Current processing methods require several minutes for every frame of data produced by the microscope and our hope is to accelerate that process. Prior to implementation however, it is necessary to decide which algorithm produces the best results. The conclusions presented in this poster give the results of our experimentation into the various phase unwrapping procedures popular in the literature [1]. Phase unwrapping using Reconfigurable Hardware In order to fully exploit the parallelism exposed in the algorithm, a sufficiently large FPGA with multiple banks of off-chip SRAM is needed. The Wildstar II Pro was selected as the reconfigurable solution that fulfils all these requirements. Reconfigurable Hardware PCI PCIBUS W ILDSTAR TM -IIPC IPro 32/64 Bits 33/66/133 M Hz 50 DDR DRAM I/O 80 20 32 32 DDR II/ Q DRII SRAM 36 Sw itches 32 32 I/O 36 36 36 36 36 DDR DRAM 80 32 32 D ifferentialPairs S ingle Ended 50 DD RII/ Q D RII SRAM DD RII/ Q DR II SRAM DDR II/ Q DRII SRAM D DRII/ Q DRII SRAM DD RII/ Q DR II SRAM D DR II/ Q DRII SRAM 36 36 36 D DR II/ Q D RII SRAM DDRII/ Q DRII SRAM 36 36 36 D D RII/ Q DRII SRAM DDR II/ Q DRII SRAM DDR II/ Q D RII SRAM 20 PE 1 VIR TE X TM IIPro XC 2VP 70,100,125 PE 2 V IR TEX TM IIPro XC 2VP 70,100,125 R ocketIO WILDSTAR™-II PRO/PCI Features of the WILDSTAR™-II PRO/PCI boards: • Uses two Xilinx® Virtex-II Pro™ FPGAs XC2V70 (33088 slices and 5904Kb BlockRAM) • 12 ports of DDR II SRAM totally 48MBytes, 2 ports of DDR SDRAM totally 256 MBytes • 11 GBytes/sec memory bandwidth This work was supported in part by CenSSIS, the Center for Subsurface Sensing and Imaging Systems, under the Engineering Research Centers Program of the National Science Foundation (Award Number EEC-9986821). Figure 2: PCG Figure 3: Quality map Figure 4: Mask Cut Figure 5: Goldsteins Figure 6: L P Norm Figure 7: Flynns Figure 1: Wrapped Phase State of the art Although no current implementation of a phase-unwrapping algorithm exists on reconfigurable hardware, much work has been done in [1] [2] to develop optimal algorithms for single-processor machines. [1] D. C. Ghiglia and M. D. Pritt, Two- Dimensional Phase Unwrapping, John Wiley & Sons, 1998. [2] C.W. Chen and H.A. Zebker, Network approaches to two- dimensional phase unwrapping, JOSA, 2000. This work is a part of the CenSSIS BioBed effort under R1, R3 and S1. Calculating the minimum L P norm phase unwrap takes several minutes per frame to process. This prevents the streaming of live video data from the microscope. Our goal is to develop a hardware/software implementation of phase unwrapping to achieve near real-time performance. R2 Fundamental Science Validating TestBEDs L1 L2 L3 R3 S1 S4 S5 S3 S2 Bio-Med Enviro-Civil R1 Optical Quadrature Microscopy Optical quadrature microscopy[3] was developed in 1997 based on techniques developed for coherent laser radar. A single coherent laser beam is split into two paths, one a reference and the other a signal path that passes through the sample under examination. Interference patterns are then captured by CCD cameras. Although the images could be taken with only two cameras, four are used to completely capture the entire signal including the conjugate intensities. After the interference fringe pattern is taken, four further steps must be undertaken to produce the final image: 1)Phase evaluation: Produces a phase-map from the spatial distribution of the phase 2)Phase unwrapping: Assigns integer multiples to the phase values 3)Term elimination: Mathematical removal of setup irregularities 4)Rescaling: Converts phase to another criteria such as distance Results • Figure 1 : Phase can be observed to vary between -π and π and although the embryos are visible, the magnitude of the phase difference cannot be measured without an unwrapping. • Figure 2: The PCG method produces a good unwrap except for the tendency to accumulate the phase from one corner of the image to another. Figure 3: The quality mapped solution has regions where the unwrap fails. E,g note that at the cell boundaries of the lower right embryo there is a decrease in phase rather than an increase • Figure 4: The mask cut algorithm produces diagonal flecking that is very noticeable across all unwraps. These are created by the incorrect placement of branch cuts. • Figure 5: Goldsteins algorithm can place branch- cuts in such a way that they isolate portions of the image and prevent the phase from being unwrapped correctly. • Figure 6: The minimum LP Norm algorithm produces the best solution. There are still segments that are incorrect (such as the cell wall boundaries in the lower right embryo) but overall, this is the most discontinuity-free solution. Average background noise is also minimized. • Figure 7: Flynns algorithm produces a high quality solution that can still be seen as incorrect given that the thickness of the sample should be increasing as the sample is traversed from the edge of the zona to the center of the embryo. Some cell boundaries also show up as phase decreases rather than increases. The minimum L P Norm algorithm as implemented here only finds a local minimum to the L 0 Norm problem since a globally minimum solution is provably NP-Complete [2]. However, it is still the best solution to the phase-unwrap problem in the context of the images produced by the OQM microscope. This can be verified through a simple visual analysis of the data, although a more complete analysis has been presented in the literature. The next step is to implement the minimum L P Norm algorithm on a reconfigurable platform, such as the Wildstar II Pro (shown to the left). This will involve determining Conclusions and Future Work • Differential Interference Contrast • Epi-Fluorescence • Optical Quadrature Microscopy • Confocal Reflectance & Fluorescence • Two-Photon Keck 3D Fusion Microscope • Differential Interference Contrast • Epi-Fluorescence • Optical Quadrature Microscopy Staring Mode Microscope OQM Capable Microscopes [3]
description
Phase unwrapping. Goal Accelerate the performance of the minimum L P Norm phase unwrapping algorithm using Field Programmable Gate Arrays (FPGAs). Figure 1: Wrapped Phase. Bio-Med. Enviro-Civil. S2. S3. S1. S4. S5. UNWRAP. L3. Validating TestBEDs. L2. R2. Fundamental Science. R1. - PowerPoint PPT Presentation
Transcript of Sherman Braganza , Miriam Leeser, W.C. Warger II, C.M. Warner, C. A. DiMarzio [email protected]...
Sherman Braganza , Miriam Leeser, W.C. Warger II, C.M. Warner, C. A. [email protected] [email protected]
Goal Accelerate the performance of the
minimum LP Norm phase unwrapping algorithm using Field
Programmable Gate Arrays (FPGAs)
AbstractOver the past several years, the development of coherent imaging techniques has increased dramatically and now applications such as Magnetic Resonance Imaging (MRI) and Synthetic Aperture Radar(SAR) are commonplace. At Northeastern University, a coherent imaging process known as Optical Quadrature Microscopy (OQM) has been developed for the purpose of non-invasively capturing the amplitude and phase data of an optically transparent sample. This can be used to reconstruct images of the original sample. However, sensors and basic signal processing produce a non-linearly wrapped phase lying in the range of (-,]. In the presence of noise, the unwrapping of the phase data can fail catastrophically. Robust methods have been proposed that unwrap around noisy sections thus preserving as much data as possible. Other methods that minimize noise through numerical error minimization techniques are also commonly used.
We aim to implement a phase unwrapping algorithm on reconfigurable hardware. Current processing methods require several minutes for every frame of data produced by the microscope and our hope is to accelerate that process. Prior to implementation however, it is necessary to decide which algorithm produces the best results. The conclusions presented in this poster give the results of our experimentation into the various phase unwrapping procedures popular in the literature [1].
Phase unwrappingusing Reconfigurable Hardware
In order to fully exploit the parallelism exposed in the algorithm, a sufficiently large FPGA with multiple banks of off-chip SRAM is needed. The Wildstar II Pro was selected as the reconfigurable solution that fulfils all these requirements.
Reconfigurable Hardware
PCI
PCI BUS
WILDSTARTM-II PCI Pro
32/64 Bits 33/66/133 MHz
50
DDRDRAM
I/O 80 20
32 32
DDRII/QDRIISRAM
36
Switches
32 32
I/O
36 36
36 36 36
DDRDRAM
80
32 32
DifferentialPairsSingle Ended
50
DDRII/QDRIISRAM
DDRII/QDRIISRAM
DDRII/QDRIISRAM
DDRII/QDRIISRAM
DDRII/QDRIISRAM
DDRII/QDRIISRAM
36 36 36
DDRII/QDRIISRAM
DDRII/QDRIISRAM
36 36 36
DDRII/QDRIISRAM
DDRII/QDRIISRAM
DDRII/QDRIISRAM
20
PE 1VIRTEXTM II Pro
XC2VP 70,100,125
PE 2VIRTEXTM II Pro
XC2VP 70,100,125
Rocket IO
WILDSTAR™-II PRO/PCI
Features of the WILDSTAR™-II PRO/PCI boards:
• Uses two Xilinx® Virtex-II Pro™ FPGAs XC2V70 (33088 slices and 5904Kb BlockRAM)
• 12 ports of DDR II SRAM totally 48MBytes, 2 ports of DDR SDRAM totally 256 MBytes
• 11 GBytes/sec memory bandwidth
This work was supported in part by CenSSIS, the Center for Subsurface Sensing and Imaging Systems, under the Engineering Research Centers Program of the National Science Foundation (Award Number EEC-9986821).
Figure 2: PCG Figure 3: Quality map Figure 4: Mask Cut
Figure 5: GoldsteinsFigure 6: LP Norm Figure 7: Flynns
Figure 1: Wrapped Phase
State of the artAlthough no current implementation of a phase-unwrapping algorithm exists on reconfigurable hardware, much work has been done in [1][2] to develop optimal algorithms for single-processor machines.
[1] D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping, John Wiley & Sons, 1998. [2] C.W. Chen and H.A. Zebker, Network approaches to two-dimensional phase unwrapping, JOSA, 2000.[3] W.C. Warger, Masters thesis, Northeastern University, 2005.
This work is a part of the CenSSIS BioBed effort under R1, R3 and S1. Calculating the minimum LP norm phase unwrap takes several minutes per frame to process. This prevents the streaming of live video data from the microscope. Our goal is to develop a hardware/software implementation of phase unwrapping to achieve near real-time performance.
R2FundamentalScience
ValidatingTestBEDs
L1
L2
L3
R3
S1 S4 S5S3S2Bio-Med Enviro-Civil
R1
Optical Quadrature MicroscopyOptical quadrature microscopy[3] was developed in 1997 based on techniques developed for coherent laser radar. A single coherent laser beam is split into two paths, one a reference and the other a signal path that passes through the sample under examination. Interference patterns are then captured by CCD cameras. Although the images could be taken with only two cameras, four are used to completely capture the entire signal including the conjugate intensities.
After the interference fringe pattern is taken, four further steps must be undertaken to produce the final image:
1) Phase evaluation: Produces a phase-map from the spatial distribution of the phase
2) Phase unwrapping: Assigns integer multiples to the phase values
3) Term elimination: Mathematical removal of setup irregularities
4) Rescaling: Converts phase to another criteria such as distance
Results • Figure 1 : Phase can be observed to vary between -π and π and although the embryos are visible, the magnitude of the phase difference cannot be measured without an unwrapping.
• Figure 2: The PCG method produces a good unwrap except for the tendency to accumulate the phase from one corner of the image to another.
Figure 3: The quality mapped solution has regions where the unwrap fails. E,g note that at the cell boundaries of the lower right embryo there is a decrease in phase rather than an increase
• Figure 4: The mask cut algorithm produces diagonal flecking that is very noticeable across all unwraps. These are created by the incorrect placement of branch cuts.
• Figure 5: Goldsteins algorithm can place branch-cuts in such a way that they isolate portions of the image and prevent the phase from being unwrapped correctly. • Figure 6: The minimum LP Norm algorithm produces the best solution. There are still segments that are incorrect (such as the cell wall boundaries in the lower right embryo) but overall, this is the most discontinuity-free solution. Average background noise is also minimized.
• Figure 7: Flynns algorithm produces a high quality solution that can still be seen as incorrect given that the thickness of the sample should be increasing as the sample is traversed from the edge of the zona to the center of the embryo. Some cell boundaries also show up as phase decreases rather than increases.
The minimum LP Norm algorithm as implemented here only finds a local minimum to the L0 Norm problem since a globally minimum solution is provably NP-Complete [2]. However, it is still the best solution to the phase-unwrap problem in the context of the images produced by the OQM microscope. This can be verified through a simple visual analysis of the data, although a more complete analysis has been presented in the literature.
The next step is to implement the minimum LP Norm algorithm on a reconfigurable platform, such as the Wildstar II Pro (shown to the left). This will involve determining the optimal software/hardware partition and implementing both in such a way as to get maximum speedup.
Conclusions and Future Work
• Differential Interference Contrast• Epi-Fluorescence• Optical Quadrature Microscopy• Confocal Reflectance & Fluorescence• Two-Photon
Keck 3D Fusion Microscope
• Differential Interference Contrast• Epi-Fluorescence• Optical Quadrature Microscopy
Staring Mode Microscope
OQM Capable Microscopes [3]
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