Paper Info
Title
Projections onto the epigraph set of the filtered variation function based deconvolution algorithm
Abstract
A new deconvolution algorithm based on orthogonal projections onto the hyperplanes and the epigraph set of a convex cost function is presented. In this algorithm, the convex sets corresponding to the cost function are defined by increasing the dimension of the minimization problem by one. The Filtered Variation (FV) function is used as the convex cost function in this algorithm. Since the FV cost function is a convex function in R <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</sup> , then the corresponding epigraph set is also a convex set in the lifted set in R <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N+1</sup> . At each step of the iterative deconvolution algorithm, starting with an arbitrary initial estimate in R <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N+1</sup> , first the projections onto the hyperplanes are performed to obtain the first deconvolution estimate. Then an orthogonal projection is performed onto the epigraph set of the FV cost function, in order to regularize and denoise the deconvolution estimate, in a sequential manner. The algorithm converges to the deblurred image.
Year
DOI
Venue
2016
10.1109/GlobalSIP.2016.7905805
2016 IEEE Global Conference on Signal and Information Processing (GlobalSIP)
Keywords
Field
DocType
Epigraph set of a convex cost function,deconvolution,projection onto convex sets,filtered variation
Convex conjugate,Blind deconvolution,Effective domain,Algorithm,Convex set,Convex function,Epigraph,Proper convex function,Convex analysis,Mathematics
Conference
ISSN
ISBN
Citations 
2376-4066
978-1-5090-4546-4
0
PageRank 
References 
Authors
0.34
13
2
Name
Order
Citations
PageRank
Mohammad-Reza Tofighi142.22
A. Enis Çetin2871118.56