How To Wow Your Friends in High Places

This is a follow-up to this entry that required the installation of Sedumi. Since many people find it inconvenient to do so, I decided to have a simpler configuration with only two matlab/octave files: run_me.m and SL0.m. Just install the files in your working directory. Run the run_me.m file and check the difference in reconstruction between the \ operator, the pinv operator and the SL0 solver used in compressive sensing (many more solvers can be found here). Here we have an underdetermined system of 10 linear equations and 50 variables embodied by a matrix A (gaussian). The sparsity of the signal being sought is 2, i.e. this vector has 50-2 = 48 zeros in it. 

We solve for x in y = Ax and expect to recover x with only two components and 48 zeros..

This is what we get with x = A\y

Not good.

This is what we get with x = pinv(A) y

Not good either. 

This is what we get with x = SL0(A,y,...)

Am I hearing a WOW yet ?

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