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Getting into Compressed Sensing

Getting into Compressed Sensing. Brian Welch May 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

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Getting into Compressed Sensing

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  1. Getting into Compressed Sensing Brian Welch May 18, 2010

  2. 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

  3. Demos from Michael Lustig • angio • angio_simulation • brain_2D • phantom_denoising • sheppLogan_TV • sheppLogan_TV_vdSpiral • thresholding

  4. 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”

  5. Angio (calf) Zero-filled with Density Compensation (good but noisy) CS Recon a real randomly undersampled (factor of 2) 3DFT acquisition

  6. Angio Simulation

  7. Brain 2D Zero-filled with Density Compensation L1 Wavelet Penalty

  8. Brain 2D k-space mask 201 of 512 (39.3%) phase encode lines Zero-filled with Density Compensation L1 Wavelet Penalty

  9. Phantom Denoising Noisy Phantom Compressed Sensing Result

  10. SheppLogan TV (8% sampling) Zero-filled with Density Compensation L1 TV (total variance) Penalty Original Low Resolution k-space Sampling Pattern

  11. SheppLogan TV VD Spiral Zero-filled with Density Compensation Original Compressed Sensing 160 × 160 image 16 spiral interleaves 902 sample per spiral 56.4% sampled

  12. Thresholding 1% 5% 10% 20% 30% DCT WAVELET FINITE DIFF.

  13. Thresholding 1% 5% 10% 20% 30% DCT WAVELET FINITE DIFF.

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