Document Type
Journal Article
Department/Unit
Department of Mathematics
Title
Fast nonconvex nonsmooth minimization methods for image restoration and reconstruction
Language
English
Abstract
Nonconvex nonsmooth regularization has advantages over convex regularization for restoring images with neat edges. However, its practical interest used to be limited by the difficulty of the computational stage which requires a nonconvex nonsmooth minimization. In this paper, we deal with nonconvex nonsmooth minimization methods for image restoration and reconstruction. Our theoretical results show that the solution of the nonconvex nonsmooth minimization problem is composed of constant regions surrounded by closed contours and neat edges. The main goal of this paper is to develop fast minimization algorithms to solve the nonconvex nonsmooth minimization problem. Our experimental results show that the effectiveness and efficiency of the proposed algorithms. © 2010 IEEE.
Keywords
Continuation methods, fast Fourier transform, image reconstruction, image restoration, nonconvex nonsmooth global minimization, nonconvex nonsmooth regularization, total variation
Publication Date
2010
Source Publication Title
IEEE Transactions on Image Processing
Volume
19
Issue
12
Start Page
3073
End Page
3088
Publisher
Institute of Electrical and Electronics Engineers
DOI
10.1109/TIP.2010.2052275
Link to Publisher's Edition
http://dx.doi.org/10.1109/TIP.2010.2052275
ISSN (print)
10577149
ISSN (electronic)
19410042
Recommended Citation
Nikolova, Mila, Michael K. Ng, and Chi-Pan Tam. "Fast nonconvex nonsmooth minimization methods for image restoration and reconstruction." IEEE Transactions on Image Processing 19.12 (2010): 3073-3088.