Recovery of Low rank and sparse Matrix

Code recovers a sparse (in transform domain) and low rank matrix from its lower dimension projection

This code is an implementation of Paper titled "Split Bregman algorithms for sparse/joint-sparse and low-rank signal recovery: Application in compressive hyper spectral imaging" presented in ICIP 2014.
This code solves the problem of recovering a low rank and sparse(in transform domain)matrix from its lower dimensional projections. There is no existing off the shelf algorithm for such a formulation.
Minimize (lambda1)||X||* + (lambda2)||Dx||_1 + 1/2 || A(X) - y ||_2^2

Formulated as an unconstarined nuclear norm and L1 minimization problem using Split bregman algorithm, formulation for the problem is as follows

% Minimize (lambda1)||W||* + (lambda2)||Dz||_1 + 1/2 || A(X) - y ||_2^2 + eta1/2 || W-X-B1 ||_2^2 +eta2/2 || W-Z-B2 ||_2^2

%W, Z are auxillary variable and B1, B2 are the bregman variable

Use of split bregman technique helps improve the accuracy and convergence behavior of the algorithm.