TY - JOUR
T1 - Alternating direction method for image inpainting in wavelet domains
AU - Chan, Raymond H.
AU - Yang, Junfeng
AU - Yuan, Xiaoming
N1 - Funding information:
Department of Mathematics, the Chinese Universi ty of Hong Kong, Shatin, Hong Kong (rchan@math. cuhk.edu.hk). This author’s research was supported by HKRGC grant CUHK 400510 and DAG grant 2060408.
* Department of Mathematics, Nanjing University, Nanj i ng, Jiangsu, 210093, China ([email protected]). This author’s research was supported by National Science Foundation of China grant NSFC-11001123 and the Fundamental Research Funds for the Central Universities grant 1117020305.
^ Corresponding author. Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong ([email protected]). This author’s research was supported by HKRGC grant HKBU 202610.
Publisher copyright:
Copyright © 2011 Society for Industrial and Applied Mathematics
PY - 2011/9/1
Y1 - 2011/9/1
N2 - Image inpainting in wavelet domains refers to the recovery of an image from incomplete and/or inaccurate wavelet coefficients. To reconstruct the image, total variation (TV) models have been widely used in the literature, and they produce high-quality reconstructed images. In this paper, we consider an unconstrained, TV-regularized, ℓ2-data-fitting model to recover the image. The model is solved by the alternating direction method (ADM). At each iteration, the ADM needs to solve three subproblems, all of which have closed-form solutions. The per-iteration computational cost of the ADM is dominated by two Fourier transforms and two wavelet transforms, all of which admit fast computation. Convergence of the ADM iterative scheme is readily obtained. We also discuss extensions of this ADM scheme to solving two closely related constrained models. We present numerical results to show the efficiency and stability of the ADM for solving wavelet domain image inpainting problems. Numerical results comparing the ADM with some recent algorithms are also reported.
AB - Image inpainting in wavelet domains refers to the recovery of an image from incomplete and/or inaccurate wavelet coefficients. To reconstruct the image, total variation (TV) models have been widely used in the literature, and they produce high-quality reconstructed images. In this paper, we consider an unconstrained, TV-regularized, ℓ2-data-fitting model to recover the image. The model is solved by the alternating direction method (ADM). At each iteration, the ADM needs to solve three subproblems, all of which have closed-form solutions. The per-iteration computational cost of the ADM is dominated by two Fourier transforms and two wavelet transforms, all of which admit fast computation. Convergence of the ADM iterative scheme is readily obtained. We also discuss extensions of this ADM scheme to solving two closely related constrained models. We present numerical results to show the efficiency and stability of the ADM for solving wavelet domain image inpainting problems. Numerical results comparing the ADM with some recent algorithms are also reported.
KW - Alternating direction method
KW - Augmented lagrangian method
KW - Fast fourier transform
KW - Fast wavelet transform
KW - Inpainting
KW - Total variation
KW - Wavelet
UR - http://www.scopus.com/inward/record.url?scp=80052894191&partnerID=8YFLogxK
U2 - 10.1137/100807247
DO - 10.1137/100807247
M3 - Journal article
AN - SCOPUS:80052894191
SN - 1936-4954
VL - 4
SP - 807
EP - 826
JO - SIAM Journal on Imaging Sciences
JF - SIAM Journal on Imaging Sciences
IS - 3
ER -