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Introduction to Compressed Sensing: Resources and Demos

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Explore the fundamentals of compressed sensing with a curated list of resources, including original sources from leading researchers Michael Lustig and Jeff Fessler. Access demo files for MATLAB, including simulations for MRI and image reconstruction. Learn how to set up your MATLAB environment for compressed sensing projects and delve into practical examples like angio simulations and phantom denoising. The provided links offer tools and datasets that will enhance your understanding and application of compressed sensing techniques in image processing.

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Introduction to Compressed Sensing: Resources and Demos

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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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