NDLI: A New Augmented Lagrangian Approach for $L^1$-mean Curvature Image Denoising

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Kärkkäinen, T. Myllykoski, M. Glowinski, R. Rossi, T.
Copyright Year	2015
Abstract	Variational methods are commonly used to solve noise removal problems. In this paper, we present an augmented Lagrangian-based approach that uses a discrete form of the $L^1$-norm of the mean curvature of the graph of the image as a regularizer, discretization being achieved via a finite element method. When a particular alternating direction method of multipliers is applied to the solution of the resulting saddle-point problem, this solution reduces to an iterative sequential solution of four subproblems. These subproblems are solved using Newtonâ s method, the conjugate gradient method, and a partial solution variant of the cyclic reduction method. The approach considered here differs from existing augmented Lagrangian approaches for the solution of the same problem; indeed, the augmented Lagrangian functional we use here contains three Lagrange multipliers only, and the associated augmentation terms are all quadratic. In addition to the description of the solution algorithm, this paper contains the results of numerical experiments demonstrating the performance of the novel method discussed here.
Starting Page	95
Ending Page	125
Page Count	31
File Format	PDF
DOI	10.1137/140962164
e-ISSN	19364954
Journal	SIAM Journal on Imaging Sciences (SJISBI)
Issue Number	1
Volume Number	8
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2015-01-15
Access Restriction	Subscribed
Subject Keyword	image processing augmented Lagrangian method Image processing Variational methods alternating direction methods of multipliers variational model mean curvature Surfaces in Euclidean space image denoising
Content Type	Text
Resource Type	Article

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