Adaptive Variational Method for Restoring Color Images with High Density Impulse Noise
International Journal of Computer Vision
Two-phase kernel estimation for robust motion deblurring
ECCV'10 Proceedings of the 11th European conference on Computer vision: Part I
A Unified Primal-Dual Algorithm Framework Based on Bregman Iteration
Journal of Scientific Computing
Image restoration under mixed noise using globally convex segmentation
Journal of Visual Communication and Image Representation
SIAM Journal on Scientific Computing
SIAM Journal on Imaging Sciences
Analysis and Generalizations of the Linearized Bregman Method
SIAM Journal on Imaging Sciences
A Fast Algorithm for Euler's Elastica Model Using Augmented Lagrangian Method
SIAM Journal on Imaging Sciences
A Regularization Parameter for Nonsmooth Tikhonov Regularization
SIAM Journal on Scientific Computing
Alternating Direction Method for Image Inpainting in Wavelet Domains
SIAM Journal on Imaging Sciences
Augmented Lagrangian Method for Generalized TV-Stokes Model
Journal of Scientific Computing
Scalable Video Coding Using Compressive Sensing
Bell Labs Technical Journal
Journal of Mathematical Imaging and Vision
Proximity algorithms for the L1/TV image denoising model
Advances in Computational Mathematics
An alternating direction method for second-order conic programming
Computers and Operations Research
An efficient ADMM algorithm for multidimensional anisotropic total variation regularization problems
Proceedings of the 19th ACM SIGKDD international conference on Knowledge discovery and data mining
Dictionary learning based impulse noise removal via L1-L1 minimization
Signal Processing
Recovering low-rank matrices from corrupted observations via the linear conjugate gradient algorithm
Journal of Computational and Applied Mathematics
A fixed-point augmented Lagrangian method for total variation minimization problems
Journal of Visual Communication and Image Representation
Hybrid regularization image deblurring in the presence of impulsive noise
Journal of Visual Communication and Image Representation
Robust blind motion deblurring using near-infrared flash image
Journal of Visual Communication and Image Representation
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We extend the alternating minimization algorithm recently proposed in [Y. Wang, J. Yang, W. Yin, and Y. Zhang, SIAM J. Imag. Sci., 1 (2008), pp. 248-272]; [J. Yang, W. Yin, Y. Zhang, and Y. Wang, SIAM J. Imag. Sci., 2 (2009), pp. 569-592] to the case of recovering blurry multichannel (color) images corrupted by impulsive rather than Gaussian noise. The algorithm minimizes the sum of a multichannel extension of total variation and a data fidelity term measured in the $\ell_1$-norm, and is applicable to both salt-and-pepper and random-valued impulsive noise. We derive the algorithm by applying the well-known quadratic penalty function technique and prove attractive convergence properties, including finite convergence for some variables and $q$-linear convergence rate. Under periodic boundary conditions, the main computational requirements of the algorithm are fast Fourier transforms and a low-complexity Gaussian elimination procedure. Numerical results on images with different blurs and impulsive noise are presented to demonstrate the efficiency of the algorithm. In addition, it is numerically compared to the least absolute deviation method [H. Y. Fu, M. K. Ng, M. Nikolova, and J. L. Barlow, SIAM J. Sci. Comput., 27 (2006), pp. 1881-1902] and the two-phase method [J. F. Cai, R. Chan, and M. Nikolova, AIMS J. Inverse Problems and Imaging, 2 (2008), pp. 187-204] for recovering grayscale images. We also present results of recovering multichannel images.