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arXiv · 1402.2088

Signal Reconstruction Framework Based On Projections Onto Epigraph Set Of A Convex Cost Function (PESC)

Mohammad Tofighi·Kivanc Kose·A. Enis Cetin
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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 $R^N$, 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.

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Mohammad Tofighi, Kivanc Kose, A. Enis Cetin. 2014-02-10. Signal Reconstruction Framework Based On Projections Onto Epigraph Set Of A Convex Cost Function (PESC). https://arxiv.org/abs/1402.2088

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