Denoising using projections onto the epigraph set of convex cost functions

Date
2014
Authors
Tofighi, Mohammad
Köse, K.
Çetin, A. Enis
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Source Title
Proceedings of the International Conference on Image Processing, IEEE 2014
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Publisher
IEEE
Volume
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Pages
2709 - 2713
Language
English
Type
Conference Paper
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Abstract

A new denoising algorithm based on 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 feasibility sets corresponding to the cost function using the epigraph concept are defined. As the utilized cost function is a convex function in RN, the corresponding epigraph set is also a convex set in RN+1. The denoising algorithm starts with an arbitrary initial estimate in RN+1. At each step of the iterative denoising, an orthogonal projection is performed onto one of the constraint sets associated with the cost function in a sequential manner. The method provides globally optimal solutions for total-variation, ℓ1, ℓ2, and entropic cost functions.1

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Keywords
Denoising, Epigraph of a cost function, Projection onto convex sets, Image denoising, Iterative methods, Orthogonal functions, Convex cost function, Orthogonal projection
Citation
Published Version (Please cite this version)