Projections onto convex sets (POCS) based optimization by lifting

buir.contributor.authorÇetin, A. Enis
buir.contributor.orcidÇetin, A. Enis|0000-0002-3449-1958
dc.contributor.authorÇetin, A. Enisen_US
dc.contributor.authorBozkurt, Alicanen_US
dc.contributor.authorGünay, Osmanen_US
dc.contributor.authorHabiboglu, Yusuf Hakanen_US
dc.contributor.authorKöse, K.en_US
dc.contributor.authorOnaran, İbrahimen_US
dc.contributor.authorTofighi, Mohammaden_US
dc.contributor.authorSevimli, Rasim Akınen_US
dc.coverage.spatialAustin, TX, USAen_US
dc.departmentDepartment of Electrical and Electronics Engineeringen_US
dc.descriptionDate of Conference: 3-5 Dec. 2013en_US
dc.description.abstractA new optimization technique based on the projections onto convex space (POCS) framework for solving convex and some non-convex optimization problems are presented. The dimension of the minimization problem is lifted by one and sets corresponding to the cost function are defined. If the cost function is a convex function in RN the corresponding set which is the epigraph of the cost function is also a convex set in RN+1. The iterative optimization approach starts with an arbitrary initial estimate in R N+1 and an orthogonal projection is performed onto one of the sets in a sequential manner at each step of the optimization problem. The method provides globally optimal solutions in total-variation, filtered variation, l1, and entropic cost functions. It is also experimentally observed that cost functions based on lp; p < 1 may be handled by using the supporting hyperplane concept. The new POCS based method can be used in image deblurring, restoration and compressive sensing problems. © 2013 IEEE.en_US
dc.source.title2013 IEEE Global Conference on Signal and Information Processingen_US
dc.subjectCompressive sensingen_US
dc.subjectIterative Optimizationen_US
dc.subjectMinimization problemsen_US
dc.subjectNonconvex optimizationen_US
dc.subjectOptimization problemsen_US
dc.subjectOptimization techniquesen_US
dc.subjectOrthogonal projectionen_US
dc.subjectProjections onto convex setsen_US
dc.subjectConvex optimizationen_US
dc.subjectCost functionsen_US
dc.subjectData processingen_US
dc.subjectImage enhancementen_US
dc.subjectIterative methodsen_US
dc.subjectSet theoryen_US
dc.titleProjections onto convex sets (POCS) based optimization by liftingen_US
dc.typeConference Paperen_US
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