TY - JOUR
T1 - Solving Constrained Total-variation Image Restoration and Reconstruction Problems via Alternating Direction Methods
AU - Ng, Michael K.
AU - Weiss, Pierre
AU - Yuan, Xiaoming
N1 - Funding information:
Centre for Mathematical Imaging and Vision and Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong ([email protected]). Research supported in part by HKRGC grants and HKBU Faculty Research grants.
§ Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong. Research supported in part by an HKRGC grant and NSFC grant 10701055.
Publisher copyright:
Copyright © 2010 Society for Industrial and Applied Mathematics
PY - 2010/8/31
Y1 - 2010/8/31
N2 - In this paper, we study alternating direction methods for solving constrained total-variation image restoration and reconstruction problems. Alternating direction methods can be implementable variants of the classical augmented Lagrangian method for optimization problems with separable structures and linear constraints. The proposed framework allows us to solve problems of image restoration, impulse noise removal, inpainting, and image cartoon+texture decomposition. As the constrained model is employed, we need only to input the noise level, and the estimation of the regularization parameter is not required in these imaging problems. Experimental results for such imaging problems are presented to illustrate the effectiveness of the proposed method. We show that the alternating direction method is very efficient for solving image restoration and reconstruction problems.
AB - In this paper, we study alternating direction methods for solving constrained total-variation image restoration and reconstruction problems. Alternating direction methods can be implementable variants of the classical augmented Lagrangian method for optimization problems with separable structures and linear constraints. The proposed framework allows us to solve problems of image restoration, impulse noise removal, inpainting, and image cartoon+texture decomposition. As the constrained model is employed, we need only to input the noise level, and the estimation of the regularization parameter is not required in these imaging problems. Experimental results for such imaging problems are presented to illustrate the effectiveness of the proposed method. We show that the alternating direction method is very efficient for solving image restoration and reconstruction problems.
KW - Alternating direction method
KW - Augmented Lagrangian
KW - Image reconstruction
KW - Image restoration
KW - Total-variation
UR - http://www.scopus.com/inward/record.url?scp=78149331304&partnerID=8YFLogxK
U2 - 10.1137/090774823
DO - 10.1137/090774823
M3 - Journal article
AN - SCOPUS:78149331304
SN - 1064-8275
VL - 32
SP - 2710
EP - 2736
JO - SIAM Journal on Scientific Computing
JF - SIAM Journal on Scientific Computing
IS - 5
ER -