A swarm based heuristic for sparse image recovery

This paper discusses the Compressive Sampling framework as an application for sparse representation (factorization) and recovery of images over an over-complete basis (dictionary). Compressive Sampling is a novel new area which asserts that one can recover images of interest, with much fewer measurements than were originally thought necessary, by searching for the sparsest representation of an image over an over-complete dictionary. This task is achieved by optimizing an objective function that includes two terms: one that measures the image reconstruction error and another that measures the sparsity level. We present and discuss a new swarm based heuristic for sparse image approximation using the Discrete Fourier Transform to enhance its level of sparsity. Our experimental results on reference images demonstrate the good performance of the proposed heuristic over other standard sparse recovery methods (L1-Magic and FOCUSS packages), in a noiseless environment using much fewer measurements. Finally, we discuss possible extensions of the heuristic in noisy environments and weakly sparse images as a realistic improvement with much higher applicability.