Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/31863
Title: Non-Lipschitz lp-regularization and box constrained model for image restoration
Authors: Chen, X 
Ng, MK
Zhang, C
Keywords: Box constraints
image restoration
non-Lipschitz
nonsmooth and nonconvex
regularization
Issue Date: 2012
Publisher: Institute of Electrical and Electronics Engineers
Source: IEEE transactions on image processing, 2012, v. 21, no. 12, 6307860, p. 4709-4721 How to cite?
Journal: IEEE transactions on image processing 
Abstract: Nonsmooth nonconvex regularization has remarkable advantages for the restoration of piecewise constant images. Constrained optimization can improve the image restoration using a priori information. In this paper, we study regularized nonsmooth nonconvex minimization with box constraints for image restoration. We present a computable positive constant θ for using nonconvex nonsmooth regularization, and show that the difference between each pixel and its four adjacent neighbors is either 0 or larger than θ in the recovered image. Moreover, we give an explicit form of θ for the box-constrained image restoration model with the non-Lipschitz nonconvex l p-norm (0<p<1) regularization. Our theoretical results show that any local minimizer of this imaging restoration problem is composed of constant regions surrounded by closed contours and edges. Numerical examples are presented to validate the theoretical results, and show that the proposed model can recover image restoration results very well.
URI: http://hdl.handle.net/10397/31863
ISSN: 1057-7149
EISSN: 1941-0042
DOI: 10.1109/TIP.2012.2214051
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