Transcript 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
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-forcompressed-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 Penalty
k-space mask
201 of 512 (39.3%) phase encode lines
Phantom Denoising
Noisy Phantom
Compressed Sensing Result
SheppLogan TV (8% sampling)
Original
k-space
Sampling
Pattern
Low Resolution
Zero-filled with
Density
Compensation
L1 TV (total variance)
Penalty
SheppLogan TV VD Spiral
Original
160 × 160 image
16 spiral interleaves
902 sample per spiral
56.4% sampled
Zero-filled with Density
Compensation
Compressed Sensing
Thresholding
FINITE DIFF.
WAVELET
DCT
1%
5%
10%
20%
30%
Thresholding
FINITE DIFF.
WAVELET
DCT
1%
5%
10%
20%
30%