Getting into Compressed Sensing

Brian WelchMay 18, 2010

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

Demos from Michael Lustig

• angio• angio_simulation• brain_2D• phantom_denoising• sheppLogan_TV• sheppLogan_TV_vdSpiral• thresholding

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”

Angio (calf)

Zero-filled with Density Compensation(good but noisy)

CS Recon

a real randomly undersampled (factor of 2) 3DFT acquisition

Angio Simulation

Brain 2D

Zero-filled with Density Compensation L1 Wavelet Penalty

Brain 2D

Zero-filled with Density Compensation

L1 Wavelet Penaltyk-space mask

201 of 512 (39.3%) phase encode lines

Phantom Denoising

Noisy Phantom Compressed Sensing Result

SheppLogan TV (8% sampling)Zero-filled with

Density Compensation

L1 TV (total variance) PenaltyLow ResolutionOriginal

k-spaceSamplingPattern

SheppLogan TV VD SpiralZero-filled with Density

Compensation Compressed SensingOriginal

160 × 160 image16 spiral interleaves902 sample per spiral56.4% sampled

Thresholding1% 5% 10% 20% 30%

Thresholding1% 5% 10% 20% 30%