Penalty Functions Derived From Monotone Mappings

被引：18

作者：

Bayram, Ilker ^{[1
]}

机构：

[1] Istanbul Tech Univ, Dept Elect & Commun Engn, Istanbul 34469, Turkey

来源：

IEEE SIGNAL PROCESSING LETTERS | 2015年 / 22卷 / 03期

关键词：

Hard threshold; monotone denoising operator; non-convex penalty; weakly convex; ALGORITHM;

D O I：

10.1109/LSP.2014.2357681

中图分类号：

TM [电工技术]; TN [电子技术、通信技术];

学科分类号：

0808 ; 0809 ;

摘要：

We consider the problem of constructing a penalty function associated with a given monotone function. We provide a construction that allows the monotone function to be discontinuous or bounded. We show that, although the penalty may be nonconvex, it is weakly convex. We briefly discuss the implications for iterative solutions of linear inverse problems.

引用

页码：265 / 269

页数：5

共 19 条

[1] Regularization of wavelet approximations - Rejoinder [J].

Antoniadis, A ;

Fan, J .

JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION, 2001, 96 (455) :964-967

[2]

CHARTRAND R, 2014, NEURAL COMPUT

[3]

CLARKE F. H., 1990, Classics Appl. Math., V5, DOI [10.1137/1.9781611971309, DOI 10.1137/1.9781611971309]

[4] Signal recovery by proximal forward-backward splitting [J].

Combettes, PL ;

Wajs, VR .

MULTISCALE MODELING & SIMULATION, 2005, 4 (04) :1168-1200

[5] An iterative thresholding algorithm for linear inverse problems with a sparsity constraint [J].

Daubechies, I ;

Defrise, M ;

De Mol, C .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2004, 57 (11) :1413-1457

[6]

DONOHO D, 2004, ADV NEURAL INFORMATI, V16

[7]

ELAD M, 2007, P SPIE WAV 12, DOI DOI 10.1109/TASL.2006.885253

[8] Variable selection via nonconcave penalized likelihood and its oracle properties [J].

Fan, JQ ;

Li, RZ .

JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION, 2001, 96 (456) :1348-1360

[9] An EM algorithm for wavelet-based image restoration [J].

Figueiredo, MAT ;

Nowak, RD .

IEEE TRANSACTIONS ON IMAGE PROCESSING, 2003, 12 (08) :906-916

[10]

Hiriart-Urruty Jean-Baptiste, 2004, Fundamentals of convex analysis

← 1 2 →