Non-convex group sparsity: Application to color imaging

This work investigates a group-sparse solution to the under-determined system of linear equations b=Ax where the unknown x is formed of a group of vectors x_i´s. A group-sparse solution has only a few x_i vectors as non-zeroes while the rest are zeroes. To seek a group-sparse solution generally a convex optimization problem is solved. Such an optimization criterion is unsuitable when the system is highly under-determined or when some of the vector x_i´s are themselves sparse. For such cases, we propose an alternate non-convex optimization problem. Simulation results show that the proposed method yields significantly improved results (2 orders of magnitude) over the standard method. We also apply the proposed group-sparse optimization in a novel fashion to the problem of color imaging. The new method shows an improvement of more than 1dB over the standard method.