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
Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion
Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion
Computational Methods for Inverse Problems
Computational Methods for Inverse Problems
Wavelets and curvelets for image deconvolution: a combined approach
Signal Processing - Special section: Security of data hiding technologies
Inverse Problem Theory and Methods for Model Parameter Estimation
Inverse Problem Theory and Methods for Model Parameter Estimation
Morphological Diversity and Sparsity for Multichannel Data Restoration
Journal of Mathematical Imaging and Vision
Compressive sensing reconstruction with prior information by iteratively reweighted least-squares
IEEE Transactions on Signal Processing
Improved Total Variation-Type Regularization Using Higher Order Edge Detectors
SIAM Journal on Imaging Sciences
Sparse signal reconstruction from limited data using FOCUSS: are-weighted minimum norm algorithm
IEEE Transactions on Signal Processing
IEEE Transactions on Information Theory
Deterministic edge-preserving regularization in computed imaging
IEEE Transactions on Image Processing
Simultaneous structure and texture image inpainting
IEEE Transactions on Image Processing
Image decomposition via the combination of sparse representations and a variational approach
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
A General Framework for Sparsity-Based Denoising and Inversion
IEEE Transactions on Signal Processing
A Signal Processing Approach to Generalized 1-D Total Variation
IEEE Transactions on Signal Processing
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This paper introduces a novel method to combine total variation and @?"2 regularizations to reconstruct piecewise smooth signals. The main idea is to consider the signal as a sum of two components: a piecewise constant component and a smooth component. For the solution of ill-posed problems, the Tikhonov method with a special stabilizer in the form of a sum of two different stabilizers is used: the total variation for the first component and the Sobolev norm for the second one. An iteratively re-weighted least squares technique is used as a fast and an efficient algorithm for minimization of the Tikhonov functional. A method is also presented for determining the regularization parameters. Numerical experiments, among the many performed, in denoising, deblurring, and compressed sensing demonstrate high performance of the new regularization for reconstruction of piecewise-smooth solutions with sharp discontinuities.