getting into compressed sensing brian welch may 18, 2010
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Getting into Compressed Sensing
Brian WelchMay 18, 2010
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Some downloads I have found• Already collected at this link:
– http://vuiis.vanderbilt.edu/~welcheb/compressed%20sensing/
• Original sources– Michael (Mikki) Lustig http://www.stanford.edu/~mlustig/SparseMRI.html– Jeff Fessler http://www.eecs.umich.edu/~fessler/code/index.html– Stanford Wavelab http://www-stat.stanford.edu/~wavelab/Wavelab_850/download.html– Sparsity Toolbox http://www.mathworks.com/matlabcentral/fileexchange/16204 – Another compressed sensing Matlab File Exchange posting :
http://www.mathworks.com/matlabcentral/fileexchange/25680-coordinate-descent-for-compressed-sensing
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Demos from Michael Lustig
• angio• angio_simulation• brain_2D• phantom_denoising• sheppLogan_TV• sheppLogan_TV_vdSpiral• thresholding
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Getting Lustig’s Demos to Run• Installed Matlab 2010a for the Mac
– available at smb://vuiis.vanderbilt.edu/software/Matlab/Matlab_R2010a/R2010a_UNIX.iso– Use smb://vuiis.vanderbilt.edu/software/Matlab/Matlab_R2010a/fik.txt as install key– Use smb://vuiis.vanderbilt.edu/software/Matlab/Matlab_R2010a/network.lic as license file
• Installed Stanford Wavelab850– Right click and “show package contents” of /Applications/MATLAB_R2010a.app– Unzip WAVELAB850.ZIP to /Applications/MATLAB_R2010a.app/toolbox/Wavelab850/– Copy (or append) /Applications/MATLAB_R2010a.app/toolbox/Wavelab850/startup.m to ~/Documents/MATLAB/startup.m– In Matlab
• cd(matlabroot)• cd(‘toolbox/Wavelab850/’)• Run Wavepath.m• Run InstallMEX.m (must have Mac Xcode [gcc compiler] installed)
• Installed Jeff Fessler’s recon Matlab tools– Unzipped fessler.tgz to ~/Documents/MATLAB/irt– In Matlab
• cd(‘~/Documents/MATLAB/irt/’)• Run setup.m
• Installed Michael Lustig’s Sparse_MRI– Unzipped sparseMRI_v0.2.tar.gz to ~/Documents/MATLAB/sparseMRI_v0.2/– “File -> Set Path -> Add with Subfolders” ; select ~/Documents/MATLAB/sparseMRI_v0.2/ ; click “Save”; click “Close”
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Angio (calf)
Zero-filled with Density Compensation(good but noisy)
CS Recon
a real randomly undersampled (factor of 2) 3DFT acquisition
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Angio Simulation
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Brain 2D
Zero-filled with Density Compensation L1 Wavelet Penalty
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Brain 2D
Zero-filled with Density Compensation
L1 Wavelet Penaltyk-space mask
201 of 512 (39.3%) phase encode lines
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Phantom Denoising
Noisy Phantom Compressed Sensing Result
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SheppLogan TV (8% sampling)Zero-filled with
Density Compensation
L1 TV (total variance) PenaltyLow ResolutionOriginal
k-spaceSamplingPattern
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SheppLogan TV VD SpiralZero-filled with Density
Compensation Compressed SensingOriginal
160 × 160 image16 spiral interleaves902 sample per spiral56.4% sampled
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Thresholding1% 5% 10% 20% 30%
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Thresholding1% 5% 10% 20% 30%