Signal Reconstruction Framework Based On Projections Onto Epigraph Set   Of A Convex Cost Function (PESC)
  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 $R^N$, 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. 
Mohammad Tofighi, Kivanc Kose, A. Enis Cetin
math.OC cs.CV