Signal Reconstruction Framework Based On Projections Onto Epigraph Set Of A Convex Cost Function (PESC)
arXiv:1402.2088
Abstract
A new signal processing framework based on making orthogonal Projections onto the Epigraph Set of a Convex cost function (PESC) is developed. In this way it is possible to solve convex optimization problems using the well-known Projections onto Convex Set (POCS) approach. In this algorithm, the dimension of the minimization problem is lifted by one and a convex set corresponding to the epigraph of the cost function is defined. If the cost function is a convex function in , the corresponding epigraph set is also a convex set in R^{N+1}. The PESC method provides globally optimal solutions for total-variation (TV), filtered variation (FV), L_1, L_2, and entropic cost function based convex optimization problems. In this article, the PESC based denoising and compressive sensing algorithms are developed. Simulation examples are presented.
Submitted to IEEE Transactions on Image Processing on 7th Jan 2014. arXiv admin note: substantial text overlap with arXiv:1309.0700, arXiv:1306.2516