Projections onto convex sets (POCS) based optimization by lifting
2013 IEEE Global Conference on Signal and Information Processing
Item Usage Stats
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 ...