Nonlinear total variation based noise removal algorithms
Proceedings of the eleventh annual international conference of the Center for Nonlinear Studies on Experimental mathematics : computational issues in nonlinear science: computational issues in nonlinear science
Recovery of blocky images from noisy and blurred data
SIAM Journal on Applied Mathematics
A Non-Local Algorithm for Image Denoising
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 2 - Volume 02
Smooth adaptation by sigmoid shrinkage
Journal on Image and Video Processing
Wavelet-based image estimation: an empirical Bayes approach using Jeffrey's noninformative prior
IEEE Transactions on Image Processing
Image denoising using scale mixtures of Gaussians in the wavelet domain
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
An improved image denoising model based on the directed diffusion equation
Computers & Mathematics with Applications
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The total variation-based image denoising model has been generalized and extended in numerous ways, improving its performance in different contexts. We propose a new penalty function motivated by the recent progress in the statistical literature on high-dimensional variable selection. Using a particular instantiation of the majorization-minimization algorithm, the optimization problem can be efficiently solved and the computational procedure realized is similar to the spatially adaptive total variation model. Our two-pixel image model shows theoretically that the new penalty function solves the bias problem inherent in the total variation model. The superior performance of the new penalty function is demonstrated through several experiments. Our investigation is limited to ''blocky'' images which have small total variation.