Deconvolution using projections onto the epigraph set of a convex cost function

Date
2014
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Source Title
Proceedings of the 22nd Signal Processing and Communications Applications Conference, SIU 2014
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Publisher
IEEE
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1638 - 1641
Language
Turkish
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Abstract

A new deconvolution algorithm based on making orthogonal projections onto the epigraph set of a convex cost function is presented. In this algorithm, the dimension of the minimization problem is lifted by one and sets corresponding to the cost function and observations are defined. If the utilized cost function is convex in RN, the corresponding epigraph set is also convex in RN+1. The deconvolution algorithm starts with an arbitrary initial estimate in RN+1. At each iteration cycle of the algorithm, first deconvolution projections are performed onto the hyperplanes representing observations, then an orthogonal projection is performed onto epigraph of the cost function. The method provides globally optimal solutions for total variation, l1, l2, and entropic cost functions.

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