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The Feasibility Pump is an effective heuristic method for solving mixed integer optimization programs. In this paper the algorithm is adapted for finding the sparse representation of signals affected by Laplacian noise. Two adaptations of the algorithm, regularized and nonregularized, are proposed, tested, and compared against the regularized least absolute deviation (RLAD) model. The obtained results show that the addition of the regularization factor always improves the algorithm. The regularized version of the algorithm also offers better results than the RLAD model in all cases. The Feasibility Pump recovers the sparse representation with good accuracy while using a very small computation time when compared with other mixed integer methods.

Feasibility Pump Algorithm for Sparse Representation under Laplacian Noise