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
An Algorithm for Total Variation Minimization and Applications
Journal of Mathematical Imaging and Vision
Bregman Iterative Algorithms for $\ell_1$-Minimization with Applications to Compressed Sensing
SIAM Journal on Imaging Sciences
The Split Bregman Method for L1-Regularized Problems
SIAM Journal on Imaging Sciences
Deblurring Poissonian images by split Bregman techniques
Journal of Visual Communication and Image Representation
Geometric Applications of the Split Bregman Method: Segmentation and Surface Reconstruction
Journal of Scientific Computing
Variational denoising of partly textured images by spatially varying constraints
IEEE Transactions on Image Processing
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The split Bregman iteration is an efficient tool for solving the total variation regularized minimization problems and has received considerable attention in recent years. In denoising case, it can remove noise well, but fails to preserve textures efficiently. In this paper, we reinterpret the split Bregman iteration from the perspective of function matching, and reveal the reason why it can not preserve textures well. To improve the performance of texture preservation, we develop a relaxed split Bregman iteration for total variation regularized image denoising. Numerical results show that for partly textured images, the new method can remove noise in the non-textured region and preserve textures in the textured region adaptively, and therefore it can improve the result both visually and in terms of the peak signal to noise ratio efficiently.