Document Type

Journal Article

Department/Unit

Department of Mathematics

Title

Lagrangian multipliers and split Bregman methods for minimization problems constrained on Sn-1

Language

English

Abstract

The numerical methods of total variation (TV) model for image denoising, especially Rudin-Osher-Fatemi (ROF) model, is widely studied in the literature. However, the S n-1 constrained counterpart is less addressed. The classical gradient descent method for the constrained problem is limited in two aspects: one is the small time step size to ensure stability; the other is that the data must be projected onto S n-1 during evolution since the unit norm constraint is poorly satisfied. In order to avoid these drawbacks, in this paper, we propose two alternative numerical methods based on the Lagrangian multipliers and split Bregman methods. Both algorithms are efficient and easy to implement. A number of experiments demonstrate that the proposed algorithms are quite effective in denoising of data constrained on S 1 or S 2, including general direction data diffusion and chromaticity denoising. © 2012 Elsevier Inc. All rights reserved.

Keywords

Lagrangian method, Split Bregman method, Total variation

Publication Date

2012

Source Publication Title

Journal of Visual Communication and Image Representation

Volume

23

Issue

7

Start Page

1041

End Page

1050

Publisher

Elsevier

DOI

10.1016/j.jvcir.2012.07.002

Link to Publisher's Edition

http://dx.doi.org/10.1016/j.jvcir.2012.07.002

ISSN (print)

10473203

ISSN (electronic)

10959076

This document is currently not available here.

Share

COinS