CoSaMP and OMP for sparse recovery

Orthogonal Matching Pursuit (OMP) and Compressive Sampling Matched Pursuit (CoSaMP).

Orthogonal matching Pursuit (OMP) and Compressive Sampling Matched Pursuit (CoSaMP) algorithm (see Needell and Tropp's 2008 paper http://arxiv.org/abs/0803.2392 ). This implementation allows several variants, and it also allows you to specify a matrix via function handles (useful if your matrix represents an FFT or similar).
A demo code shows how to use both the OMP.m and CoSaMP.m functions.
OMP and CoSaMP are useful for sparse recovery problems; in particular, they can be used for compressed sensing (aka compressive sampling), image denoising and deblurring, seismic tomography problems, MRI, etc.

Another good OMP implementation (C++, Matlab) is here:
http://www.di.ens.fr/willow/SPAMS/
(Updated, March 2012: SPAMS now has python and R bindings as well)

And a CoSaMP implementation (I haven't tested):
http://media.aau.dk/null_space_pursuits/2011/07/a-few-corrections-to-cosamp-and-sp-matlab.html
Edit: that CoSaMP implementation mentioned above is buggy. Read this:
http://media.aau.dk/null_space_pursuits/2011/08/cosamp-and-cosaomp.html

Update, Feb 2012: for a blog discussion of several way to implement CoSaMP, see this website:
http://media.aau.dk/null_space_pursuits/2012/02/speedups-in-omp-implementations.html