GeLMA is an algorithm to solve an underdetermined linear system Ax=b, when x is sparse. Its convergence analysis was discussed in this paper. You will also need this file.
In the paper Illumination strategies for intensity-only imaging, we used this file to generate data. It is the main file of the algorithm to image sparse scatterers in homogeneous media with amplitude measurements only. Run it in the command line in MATLAB. You will need two additional files: the GeLMA subroutine and the initialization.