Fast nonconvex nonsmooth minimization methods for image restoration and reconstruction

Mila Nikolova*, Kwok Po NG, Chi Pan Tam

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

180 Citations (Scopus)

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.

Original languageEnglish
Article number5483167
Pages (from-to)3073-3088
Number of pages16
JournalIEEE Transactions on Image Processing
Volume19
Issue number12
DOIs
Publication statusPublished - Dec 2010

Scopus Subject Areas

  • Software
  • Computer Graphics and Computer-Aided Design

User-Defined Keywords

  • Continuation methods
  • fast Fourier transform
  • image reconstruction
  • image restoration
  • nonconvex nonsmooth global minimization
  • nonconvex nonsmooth regularization
  • total variation

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