On Some Iterative Concepts for Image Restoration

[1]  Antonin Chambolle,et al.  A l1-Unified Variational Framework for Image Restoration , 2004, ECCV.

[2]  Stanley Osher,et al.  Modeling Textures with Total Variation Minimization and Oscillating Patterns in Image Processing , 2003, J. Sci. Comput..

[3]  Z. Opial Weak convergence of the sequence of successive approximations for nonexpansive mappings , 1967 .

[4]  Luminita A. Vese,et al.  Image Decomposition Using Total Variation and div(BMO) , 2005, Multiscale Model. Simul..

[5]  Ingrid Daubechies,et al.  Wavelet-based image decomposition by variational functionals , 2004, SPIE Optics East.

[6]  Ingrid Daubechies,et al.  Variational image restoration by means of wavelets: simultaneous decomposition , 2005 .

[7]  R. DeVore,et al.  Interpolation of Besov-Spaces , 1988 .

[8]  I. Daubechies Orthonormal bases of compactly supported wavelets , 1988 .

[9]  A. Kufner,et al.  Triebel, H., Interpolation Theory, Function Spaces, Differential Operators. Berlin, VEB Deutscher Verlag der Wissenschaften 1978. 528 S., M 87,50 , 1979 .

[10]  S. Osher,et al.  IMAGE DECOMPOSITION AND RESTORATION USING TOTAL VARIATION MINIMIZATION AND THE H−1 NORM∗ , 2002 .

[11]  D. Donoho,et al.  Translation-Invariant De-Noising , 1995 .

[12]  Stanley Osher,et al.  Image Decomposition and Restoration Using Total Variation Minimization and the H1 , 2003, Multiscale Model. Simul..

[13]  H. Triebel Interpolation Theory, Function Spaces, Differential Operators , 1978 .

[14]  L. Evans Measure theory and fine properties of functions , 1992 .

[15]  Bruno Torrésani,et al.  Time-Frequency Jigsaw Puzzle: Adaptive Multiwindow and Multilayered Gabor Expansions , 2007, Int. J. Wavelets Multiresolution Inf. Process..

[16]  Donald Geman,et al.  Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[17]  Ingrid Daubechies,et al.  Ten Lectures on Wavelets , 1992 .

[18]  Jitendra Malik,et al.  Scale-Space and Edge Detection Using Anisotropic Diffusion , 1990, IEEE Trans. Pattern Anal. Mach. Intell..

[19]  Massimo Fornasier,et al.  Recovery Algorithms for Vector-Valued Data with Joint Sparsity Constraints , 2008, SIAM J. Numer. Anal..

[20]  I. Daubechies,et al.  An iterative thresholding algorithm for linear inverse problems with a sparsity constraint , 2003, math/0307152.

[21]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[22]  R. DeVore,et al.  Nonlinear Approximation and the Space BV(R2) , 1999 .

[23]  L. Rudin,et al.  Nonlinear total variation based noise removal algorithms , 1992 .

[24]  B. Jawerth,et al.  A discrete transform and decompositions of distribution spaces , 1990 .

[25]  I. Daubechiesa,et al.  Variational image restoration by means of wavelets : Simultaneous decomposition , deblurring , and denoising , 2005 .

[26]  Patrick L. Combettes,et al.  Signal Recovery by Proximal Forward-Backward Splitting , 2005, Multiscale Model. Simul..

[27]  G. Aubert,et al.  Modeling Very Oscillating Signals. Application to Image Processing , 2005 .

[28]  L. Ambrosio,et al.  Functions of Bounded Variation and Free Discontinuity Problems , 2000 .

[29]  W. Dahmen Stability of Multiscale Transformations. , 1995 .

[30]  Yves Meyer,et al.  Oscillating Patterns in Image Processing and Nonlinear Evolution Equations: The Fifteenth Dean Jacqueline B. Lewis Memorial Lectures , 2001 .

[31]  L. Vese,et al.  A Variational Method in Image Recovery , 1997 .

[32]  S. Anthoine Different Wavelet-based Approaches for the Separation of Noisy and Blurred Mixtures of Components. Application to Astrophysical Data. , 2005 .

[33]  Michael Elad,et al.  Submitted to Ieee Transactions on Image Processing Image Decomposition via the Combination of Sparse Representations and a Variational Approach , 2022 .

[34]  Felix Fernandes,et al.  Directional complex-wavelet processing , 2000, SPIE Optics + Photonics.

[35]  G. Teschke Multi-frame representations in linear inverse problems with mixed multi-constraints , 2007 .

[36]  A. Antoniadis,et al.  Wavelets and Statistics , 1995 .

[37]  N. Kingsbury Image processing with complex wavelets , 1999, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[38]  P. Lions,et al.  Image recovery via total variation minimization and related problems , 1997 .

[39]  R. DeVore,et al.  Compression of wavelet decompositions , 1992 .

[40]  Michael A. Saunders,et al.  Atomic Decomposition by Basis Pursuit , 1998, SIAM J. Sci. Comput..

[41]  Donald Geman,et al.  Constrained Restoration and the Recovery of Discontinuities , 1992, IEEE Trans. Pattern Anal. Mach. Intell..

[42]  Stanley Osher,et al.  Total variation based image restoration with free local constraints , 1994, Proceedings of 1st International Conference on Image Processing.

[43]  I. Daubechies,et al.  Iteratively solving linear inverse problems under general convex constraints , 2007 .

[44]  Michel Defrise,et al.  Inverse imaging with mixed penalties , 2004 .

[45]  Stanley Osher,et al.  Image Denoising and Decomposition with Total Variation Minimization and Oscillatory Functions , 2004, Journal of Mathematical Imaging and Vision.

[46]  I. Ekeland,et al.  Convex analysis and variational problems , 1976 .

[47]  D. Donoho,et al.  Simultaneous cartoon and texture image inpainting using morphological component analysis (MCA) , 2005 .

[48]  Bruno Torrésani,et al.  Hybrid representations for audiophonic signal encoding , 2002, Signal Process..

[49]  M. Nikolova An Algorithm for Total Variation Minimization and Applications , 2004 .

[50]  Stéphane Mallat,et al.  Characterization of Signals from Multiscale Edges , 2011, IEEE Trans. Pattern Anal. Mach. Intell..

[51]  I. Selesnick Hilbert transform pairs of wavelet bases , 2001, IEEE Signal Processing Letters.

[52]  L. Vese A Study in the BV Space of a Denoising—Deblurring Variational Problem , 2001 .

[53]  I. Daubechies,et al.  Biorthogonal bases of compactly supported wavelets , 1992 .