A Signal Processing Approach to Generalized 1-D Total Variation

被引：47

作者：

Karahanoglu, Fikret Isik ^{[1
,2
]}

Bayram, Ilker ^{[3
]}

Van De Ville, Dimitri ^{[1
,2
]}

机构：

[1] Ecole Polytech Fed Lausanne, Med Image Proc Lab MIPLAB, Inst Bioengn, CH-1016 Lausanne, Switzerland

[2] Univ Genoa, Dept Radiol & Med Informat, Vevey, Switzerland

[3] Ecole Polytech Fed Lausanne, BIG, Lausanne, Switzerland

来源：

IEEE TRANSACTIONS ON SIGNAL PROCESSING | 2011年 / 59卷 / 11期

基金：

瑞士国家科学基金会;

关键词：

Differential operators; linear systems; regularization; sparsity; total variation; TOTAL VARIATION MINIMIZATION; CARDINAL EXPONENTIAL SPLINES; CONSTRAINED TOTAL VARIATION; IMAGE-RESTORATION; PART I; ALGORITHM; REGULARIZATION; DECOMPOSITION; OPTIMIZATION; SHRINKAGE;

D O I：

10.1109/TSP.2011.2164399

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：

Total variation (TV) is a powerful method that brings great benefit for edge-preserving regularization. Despite being widely employed in image processing, it has restricted applicability for 1-D signal processing since piecewise-constant signals form a rather limited model for many applications. Here we generalize conventional TV in 1-D by extending the derivative operator, which is within the regularization term, to any linear differential operator. This provides flexibility for tailoring the approach to the presence of nontrivial linear systems and for different types of driving signals such as spike-like, piecewise-constant, and so on. Conventional TV remains a special case of this general framework. We illustrate the feasibility of the method by considering a nontrivial linear system and different types of driving signals.

引用

页码：5265 / 5274

页数：10

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