2014/08/20 by Ivan Selesnick, Ivan W. Selesnick, Ankit Parekh +2 · 1 citation
Computer Science · Engineering · #Image and Signal Denoising Methods #Photoacoustic and Ultrasonic Imaging #Sparse and Compressive Sensing Techniques
paper · doi:10.1109/lsp.2014.2349356
openalex publication_date 2014/08/20 · crossref created 2014/08/20 · crossref issued 2015/02/01 · crossref published 2015/02/01 · crossref published-print 2015/02/01 · crossref deposited 2022/01/12 · openalex created_date 2025/10/10 · crossref indexed 2026/07/30 · openalex updated_date 2026/07/31
Total variation (TV) denoising is an effective noise suppression method when the derivative of the underlying signal is known to be sparse. TV denoising is defined in terms of a convex optimization problem involving a quadratic data fidelity term and a convex regularization term. A non-convex regularizer can promote sparsity more strongly, but generally leads to a non-convex optimization problem with non-optimal local minima. This letter proposes the use of a non-convex regularizer constrained so that the total objective function to be minimized maintains its convexity. Conditions for a non-convex regularizer are given that ensure the total TV denoising objective function is convex. An efficient algorithm is given for the resulting problem.