Projections onto convex sets (POCS) based optimization by lifting
Çetin, A. Enis
Habiboglu, Yusuf Hakan
Sevimli, Rasim Akın
2013 IEEE Global Conference on Signal and Information Processing
Item Usage Stats
MetadataShow full item record
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.
Projections onto convex sets
Published Version (Please cite this version)http://dx.doi.org/10.1109/GlobalSIP.2013.6736960
Showing items related by title, author, creator and subject.
Rudloff, B.; Ulus, F.; Vanderbei, R. (Springer, 2017)In this paper, a parametric simplex algorithm for solving linear vector optimization problems (LVOPs) is presented. This algorithm can be seen as a variant of the multi-objective simplex (the Evans–Steuer) algorithm (Math ...
Urfalıoğlu, Onay; Çetin, A. Enis; Kuruoğlu, E. E. (ACM, 2008-07)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 ...
Optimal signaling and detector design for power constrained on-off keying systems in Neyman-Pearson framework Dulek, Berkan; Gezici, Sinan (IEEE, 2011)Optimal stochastic signaling and detector design are studied for power constrained on-off keying systems in the presence of additive multimodal channel noise under the Neyman-Pearson (NP) framework. The problem of jointly ...