Approximations For Solving L0-Norm Minimization Problems In Compressed Sensing
Compressed Sensing is a signal processing technique for under-sampling and optimal recovery of a signal, in particular images. It exploits the fact that natural images are sparse in some domain like the Discrete Fourier Transform or Wavelets. The sparsity of the signal can be exploited via optimization to recover it from far fewer samples than required by the Nyquist-Shannon sampling theorem. The sparsity constraint, however, is of a combinatorial nature and is not convex. We explore various methods for solving this problem via convex optimization.
Running the code
- OMP: Go to the
omp/
folder and set them
parameter inomp.m
to specify fraction of available measurements. Then runomp.m
. - SCA: Go to the
sca/
folder and set them
parameter insca.m
orscap.m
to specify fraction of available measurements, and thek
,t
,eps
, andmaxIter
parameters for controlling sparsity of the output, coarseness of the L0 norm approximation, stopping error and maximum iterations per frame respectively. Then runsca.m
orscap.m
.scap.m
is the parallel version ofsca.m
. - PD: Go to the
pd/
folder and set them
parameter inpd_parallel.m
to specify fraction of available measurements, and other parameters to run the PD reconstruction in the solvePD.m code itself.
All code has been written and tested on Matlab R2014b.
Authors
Alankar Kotwal, alankarkotwal13@gmail.com
Anand Kalvit, anandiitb12@gmail.com