Projections onto convex sets (POCS) based optimization by lifting Conference Paper
| Authors: | Cetin, A. E.; Bozkurt, A.; Gunay, O.; Habiboglu, Y. H.; Kose, K.; Onaran, I.; Tofighi, M.; Sevimli, R. A. |
| Title: | Projections onto convex sets (POCS) based optimization by lifting |
| Conference Title: | 2013 1st IEEE Global Conference on Signal and Information Processing, GlobalSIP 2013 |
| Abstract: | 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. |
| Keywords: | image enhancement; optimization; set theory; data processing; optimization problems; iterative methods; compressive sensing; iterative optimization; minimization problems; nonconvex optimization; optimization techniques; orthogonal projection; projections onto convex sets; convex optimization; cost functions |
| Journal Title | Proceedings of the 2013 IEEE Global Conference on Signal and Information Processing (GlobalSIP) |
| Conference Dates: | 2013 Dec 3-5 |
| Conference Location: | Austin, TX |
| ISBN: | 9781479902484 |
| Publisher: | IEEE |
| Location: | Austin, TX |
| Date Published: | 2013-01-01 |
| Start Page: | 623 |
| Language: | English |
| DOI: | 10.1109/GlobalSIP.2013.6736960 |
| PROVIDER: | scopus |
| DOI/URL: | |
| Notes: | 2013 IEEE Global Conference on Signal and Information Processing, GlobalSIP 2013 - Proceedings -- IEEE Global Conf. Signal Inf. Process., GlobalSIP - Proc. -- Conference code: 103051 -- Export Date: 1 May 2014 -- Art. No.: 6736960 -- Sponsors: The Institute of Electrical and Electronics Engineers (IEEE) Signal Processing Society; National Instruments; Now Publishers, Inc.; InView Corporation -- 3 December 2013 through 5 December 2013 -- Source: Scopus |
