2007 IEEE International Conference on Image Processing - San Antonio, Texas, U.S.A. - September 16-19, 2007

Technical Program

Paper Detail

Paper:MA-L4.3
Session:Image and Video Restoration
Time:Monday, September 17, 10:30 - 10:50
Presentation: Lecture
Title: TWO-STEP ALGORITHMS FOR LINEAR INVERSE PROBLEMS WITH NON-QUADRATIC REGULARIZATION
Authors: José Bioucas-Dias; Instituto Superior Técnico 
 Mário Figueiredo; Instituto Superior Técnico 
Abstract: Iterative shrinkage/thresholding (IST) algorithms have been recently proposed to handle high-dimensional convex optimization problems arising in image inverse problems (namely deconvolution) under non-quadratic regularization (e.g., total variation or sparsity inducing regularizers on wavelet representations). The convergence speed of IST algorithms depends heavily on the nature of the direct operator, being very slow when this operator is severely ill-conditioned. In this paper, we introduce a two-step version of IST (termed 2IST, pronounced ``twist") showing much faster convergence for strongly ill-conditioned operators. We give theoretical results concerning the convergence behavior of 2IST and show its effectiveness for wavelet-based and total variation image deconvolution.



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