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论文类型：期刊论文

发表时间：2012-03-01

发表刊物：JOURNAL OF COMPUTATIONAL MATHEMATICS

收录刊物：SCIE、CSCD、Scopus

卷号：30

期号：2

页面范围：177-196

ISSN号：0254-9409

关键字：Image restoration; Total variation; Newton method; Homotopy method; Correction and curve tracking

摘要：The total variation (TV) minimization problem is widely studied in image restoration. Although many alternative methods have been proposed for its solution, the Newton method remains not usable for the primal formulation due to no convergence. A previous study by Chan, Zhou and Chan [15] considered a regularization parameter continuation idea to increase the domain of convergence of the Newton method with some success but no robust parameter selection schemes. In this paper, we consider a homotopy method for the same primal TV formulation and propose to use curve tracking to select the regularization parameter adaptively. It turns out that; this idea helps to improve substantially the previous work in efficiently solving the TV Euler-Lagrange equation. The same idea is also considered for the two other methods as well as the deblurring problem, again with improvements obtained. Numerical experiments show that our new methods are robust; and fast for image restoration, even for images with large noisy-to-signal ratio.