Projections onto convex sets (POCS) based optimization by lifting
Please cite this item using this persistent URLhttp://hdl.handle.net/11693/27908
2013 IEEE Global Conference on Signal and Information Processing, GlobalSIP 2013 - Proceedings
- Conference Paper 
A 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.
Showing items related by title, author, creator and subject.
Optimal signaling and detector design for power-constrained binary communications systems over non-Gaussian channels Göken, C.; Gezici, S.; Arikan, O. (2010)In this letter, joint optimization of signal structures and detectors is studied for binary communications systems under average power constraints in the presence of additive non-Gaussian noise. First, it is observed that ...
Alper Yildirim, E. (2012)We consider linear optimization problems over the cone of copositive matrices. Such conic optimization problems, called copositive programs, arise from the reformulation of a wide variety of difficult optimization problems. ...
Urfaliog̃lu O.; Çetin, A.E.; Kuruog̃lu, E.E. (2008)A novel evolutionary global optimization approach based on adaptive covariance estimation is proposed. The proposed method samples from a multivariate Levy Skew Alpha-Stable distribution with the estimated covariance matrix ...