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
Iterative methods for total variation denoising
SIAM Journal on Scientific Computing - Special issue on iterative methods in numerical linear algebra; selected papers from the Colorado conference
A Nonlinear Primal-Dual Method for Total Variation-Based Image Restoration
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Adapted Total Variation for Artifact Free Decompression of JPEG Images
Journal of Mathematical Imaging and Vision
An adaptive algorithm for image restoration using combined penalty functions
Pattern Recognition Letters
The Application of Constrained Least Squares Estimation to Image Restoration by Digital Computer
IEEE Transactions on Computers
On the partial difference equations of mathematical physics
IBM Journal of Research and Development
Color TV: total variation methods for restoration of vector-valued images
IEEE Transactions on Image Processing
Disparity-based space-variant image deblurring
Image Communication
A Framework for Moving Least Squares Method with Total Variation Minimizing Regularization
Journal of Mathematical Imaging and Vision
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The problem for image restoration is usually reduced to a constraint optimization problem. Different choice of optimization operator leads to various restoration models, e.g. least squares model and original total variation (TV) model. The TV model and its modified version can efficiently preserve the edge of the restored image well, but there exist obvious staircases in smooth area of the restored image. To reduce those staircases, we propose a new modified TV model, by adding a constraint term for smooth area protection as a penalty function. The numerical experiment shows our model can not only preserve the edge as well as TV model, but also efficiently reduce the staircase appearing in the smooth areas. Furthermore, It is shown that the restored image by our model has higher signal-to-noise ratio, less mean square error and better visual effect than those by the least squares model and by the TV models.