Minimization methods for non-differentiable functions
Minimization methods for non-differentiable functions
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
Signal Processing - Image and Video Coding beyond Standards
Reconstruction of Wavelet Coefficients Using Total Variation Minimization
SIAM Journal on Scientific Computing
Bilateral Filtering for Gray and Color Images
ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
Smooth minimization of non-smooth functions
Mathematical Programming: Series A and B
Combined Complex Ridgelet Shrinkage and Total Variation Minimization
SIAM Journal on Scientific Computing
A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
Some First-Order Algorithms for Total Variation Based Image Restoration
Journal of Mathematical Imaging and Vision
Shearlet-based total variation diffusion for denoising
IEEE Transactions on Image Processing
A New Alternating Minimization Algorithm for Total Variation Image Reconstruction
SIAM Journal on Imaging Sciences
Tetrolet transform: A new adaptive Haar wavelet algorithm for sparse image representation
Journal of Visual Communication and Image Representation
The digital TV filter and nonlinear denoising
IEEE Transactions on Image Processing
Sparse geometric image representations with bandelets
IEEE Transactions on Image Processing
Image decomposition via the combination of sparse representations and a variational approach
IEEE Transactions on Image Processing
The contourlet transform: an efficient directional multiresolution image representation
IEEE Transactions on Image Processing
Nonlinear Regularized Reaction-Diffusion Filters for Denoising of Images With Textures
IEEE Transactions on Image Processing
Tetrolet transform: A new adaptive Haar wavelet algorithm for sparse image representation
Journal of Visual Communication and Image Representation
An envelope signal based deconvolution algorithm for ultrasound imaging
Signal Processing
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In this paper, an anisotropic total variation (ATV) minimization is combined with the new adaptive tetrolet transform for discontinuity-preserving image processing. In order to suppress the pseudo-Gibbs artefacts and to increase the regularity, the conventional shrinkage results are further processed by a total variation (TV) minimization scheme, in which only the insignificant tetrolet coefficients of the image are changed by the use of ATV constrained projection, instead of previous TV projections. Numerical experiments of piecewise-smooth images show the good performance of the proposed hybrid method to recover the shape of edges and important detailed directional components, in comparison to some existing methods.