TOTAL VARIATION DENOISINGWITH OVERLAPPING GROUP SPARSITY

This paper describes an extension to total variation denoising wherein it is assumed the first-order difference function of the un-known signal is not only sparse, but also that large values of the first-order difference function do not generally occur in isolation. This approach is designed to alleviate the staircase artifact often arising in total variation based solutions. A convex cost function is given and an iterative algorithm is derived using majorization-minimization. The algorithm is both fast converging and computationally efficient due to the use of fast solvers for banded systems. Index Terms — total variation, sparse signal processing, L1 norm, group sparsity, denoising, filter, convex optimization. 1