An efficient algorithm for total variation regularization with applications to the single pixel camera and compressive sensing

An Efficient Algorithm For Total Variation Regularization with Applications to the Single Pixel Camera and Compressive Sensing

[1]  R. Courant.  Variational methods for the solution of problems of equilibrium and vibrations , 1943 .

[2]  H. H. Rachford,et al.  The Numerical Solution of Parabolic and Elliptic Differential Equations , 1955 .

[3]  M. Sion.  On general minimax theorems , 1958 .

[4]  M. Powell.  A method for nonlinear constraints in minimization problems , 1969 .

[5]  M. Hestenes.  Multiplier and gradient methods , 1969 .

[6]  G. Robinson,et al.  Logical convolution and discrete Walsh and Fourier power spectra , 1972 .

[7]  R. Rockafellar.  The multiplier method of Hestenes and Powell applied to convex programming , 1973 .

[8]  R. Tapia.  Newton’s Method for Optimization Problems with Equality Constraints , 1974 .

[9]  R. Tapia.  Newton's Method for Problems with Equality Constraints , 1974 .

[10]  R. Tapia.  Diagonalized multiplier methods and quasi-Newton methods for constrained optimization , 1977 .

[11]  R. Byrd.  Local convergence of the diagonalized method of multipliers , 1978 .

[12]  R. Glowinski.  Lectures on Numerical Methods for Non-Linear Variational Problems , 1981 .

[13]  Dimitri P. Bertsekas,et al.  Constrained Optimization and Lagrange Multiplier Methods , 1982 .

[14]  B. Sankur,et al.  Applications of Walsh and related functions , 1986 .

[15]  F. Santosa,et al.  Linear inversion of ban limit reflection seismograms , 1986 .

[16]  L. Grippo,et al.  A nonmonotone line search technique for Newton's method , 1986 .

[17]  Paul H. Calamai,et al.  Projected gradient methods for linearly constrained problems , 1987, Math. Program..

[18]  J. Borwein,et al.  Two-Point Step Size Gradient Methods , 1988 .

[19]  S.-P. Han,et al.  A parallel projection method for solving generalized linear least-squares problems , 1988 .

[20]  H. Komiya.  Elementary proof for Sion's minimax theorem , 1988 .

[21]  Sehie Park,et al.  NONLINEAR VARIATIONAL INEQUALITIES AND FIXED POINT THEOREMS , 1989 .

[22]  D. Donoho,et al.  Uncertainty principles and signal recovery , 1989 .

[23]  M. MarcosRaydan.  Convergence properties of the Barzilai and Borwein gradient method , 1991 .

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

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

[26]  B. Logan,et al.  Signal recovery and the large sieve , 1992 .

[27]  Y. C. Pati,et al.  Orthogonal matching pursuit: recursive function approximation with applications to wavelet decomposition , 1993, Proceedings of 27th Asilomar Conference on Signals, Systems and Computers.

[28]  Stéphane Mallat,et al.  Matching pursuits with time-frequency dictionaries , 1993, IEEE Trans. Signal Process..

[29]  D. Donoho,et al.  Basis pursuit , 1994, Proceedings of 1994 28th Asilomar Conference on Signals, Systems and Computers.

[30]  Jeffrey B. Sampsell,et al.  Digital micromirror device and its application to projection displays , 1994 .

[31]  Dimitri P. Bertsekas,et al.  Nonlinear Programming , 1997 .

[32]  Donald Geman,et al.  Nonlinear image recovery with half-quadratic regularization , 1995, IEEE Trans. Image Process..

[33]  Balas K. Natarajan,et al.  Sparse Approximate Solutions to Linear Systems , 1995, SIAM J. Comput..

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

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

[36]  V. Temlyakov.  Greedy Algorithms andM-Term Approximation with Regard to Redundant Dictionaries , 1999 .

[37]  Xiaoming Huo,et al.  Uncertainty principles and ideal atomic decomposition , 2001, IEEE Trans. Inf. Theory.

[38]  R. Nowak,et al.  Fast wavelet-based image deconvolution using the EM algorithm , 2001, Conference Record of Thirty-Fifth Asilomar Conference on Signals, Systems and Computers (Cat.No.01CH37256).

[39]  Michael Elad,et al.  A generalized uncertainty principle and sparse representation in pairs of bases , 2002, IEEE Trans. Inf. Theory.

[40]  Michael Elad,et al.  Optimally sparse representation in general (nonorthogonal) dictionaries via ℓ1 minimization , 2003, Proceedings of the National Academy of Sciences of the United States of America.

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

[42]  Fionn Murtagh,et al.  Fast communication , 2002 .

[43]  Rémi Gribonval,et al.  Sparse representations in unions of bases , 2003, IEEE Trans. Inf. Theory.

[44]  Arkadi Nemirovski,et al.  On sparse representation in pairs of bases , 2003, IEEE Trans. Inf. Theory.

[45]  William W. Hager,et al.  A Nonmonotone Line Search Technique and Its Application to Unconstrained Optimization , 2004, SIAM J. Optim..

[46]  Andy M. Yip,et al.  Recent Developments in Total Variation Image Restoration , 2004 .

[47]  Joel A. Tropp,et al.  Greed is good: algorithmic results for sparse approximation , 2004, IEEE Transactions on Information Theory.

[48]  ANTONIN CHAMBOLLE,et al.  An Algorithm for Total Variation Minimization and Applications , 2004, Journal of Mathematical Imaging and Vision.

[49]  Jean-Jacques Fuchs,et al.  On sparse representations in arbitrary redundant bases , 2004, IEEE Transactions on Information Theory.

[50]  Wotao Yin,et al.  Second-order Cone Programming Methods for Total Variation-Based Image Restoration , 2005, SIAM J. Sci. Comput..

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

[52]  Yurii Nesterov,et al.  Smooth minimization of non-smooth functions , 2005, Math. Program..

[53]  R.G. Baraniuk,et al.  Distributed Compressed Sensing of Jointly Sparse Signals , 2005, Conference Record of the Thirty-Ninth Asilomar Conference onSignals, Systems and Computers, 2005..

[54]  Emmanuel J. Candès,et al.  Decoding by linear programming , 2005, IEEE Transactions on Information Theory.

[55]  D. Donoho,et al.  Neighborliness of randomly projected simplices in high dimensions. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[56]  M. Rudelson,et al.  Geometric approach to error-correcting codes and reconstruction of signals , 2005, math/0502299.

[57]  Michael Elad,et al.  Why Simple Shrinkage Is Still Relevant for Redundant Representations? , 2006, IEEE Transactions on Information Theory.

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

[59]  Emmanuel J. Candès,et al.  Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information , 2004, IEEE Transactions on Information Theory.

[60]  Richard G. Baraniuk,et al.  A new compressive imaging camera architecture using optical-domain compression , 2006, Electronic Imaging.

[61]  Richard G. Baraniuk,et al.  Compressive imaging for video representation and coding , 2006 .

[62]  Richard G. Baraniuk,et al.  An Architecture for Compressive Imaging , 2006, 2006 International Conference on Image Processing.

[63]  L. He,et al.  MR Image Reconstruction from Sparse Radial Samples Using Bregman Iteration , 2006 .

[64]  David L Donoho,et al.  Compressed sensing , 2006, IEEE Transactions on Information Theory.

[65]  Joel A. Tropp,et al.  Just relax: convex programming methods for identifying sparse signals in noise , 2006, IEEE Transactions on Information Theory.

[66]  Emmanuel J. Candès,et al.  Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies? , 2004, IEEE Transactions on Information Theory.

[67]  Pierre Vandergheynst,et al.  On the exponential convergence of matching pursuits in quasi-incoherent dictionaries , 2006, IEEE Transactions on Information Theory.

[68]  José M. Bioucas-Dias,et al.  A New TwIST: Two-Step Iterative Shrinkage/Thresholding Algorithms for Image Restoration , 2007, IEEE Transactions on Image Processing.

[69]  Richard G. Baraniuk,et al.  Theory and Implementation of an Analog-to-Information Converter using Random Demodulation , 2007, 2007 IEEE International Symposium on Circuits and Systems.

[70]  Stephen P. Boyd,et al.  Enhancing Sparsity by Reweighted ℓ1 Minimization , 2007, 0711.1612.

[71]  José M. Bioucas-Dias,et al.  Two-Step Algorithms for Linear Inverse Problems with Non-Quadratic Regularization , 2007, 2007 IEEE International Conference on Image Processing.

[72]  D. Donoho,et al.  Sparse MRI: The application of compressed sensing for rapid MR imaging , 2007, Magnetic resonance in medicine.

[73]  Yin Zhang,et al.  Fixed-Point Continuation for l1-Minimization: Methodology and Convergence , 2008, SIAM J. Optim..

[74]  E.L. Jacobs,et al.  Compressive sensing applied to homeland security , 2008, 2008 IEEE Sensors Applications Symposium.

[75]  R. Nowak,et al.  Compressed Sensing for Networked Data , 2008, IEEE Signal Processing Magazine.

[76]  Ting Sun,et al.  Single-pixel imaging via compressive sampling , 2008, IEEE Signal Process. Mag..

[77]  Yin Zhang.  On Theory of Compressive Sensing via L_1-Minimization: Simple Derivations and Extensions , 2008 .

[78]  Junfeng Yang,et al.  A Fast TVL1-L2 Minimization Algorithm for Signal Reconstruction from Partial Fourier Data , 2008 .

[79]  Junfeng Yang,et al.  A New Alternating Minimization Algorithm for Total Variation Image Reconstruction , 2008, SIAM J. Imaging Sci..

[80]  Junfeng Yang,et al.  An Efficient TVL1 Algorithm for Deblurring Multichannel Images Corrupted by Impulsive Noise , 2009, SIAM J. Sci. Comput..

[81]  Junfeng Yang,et al.  A Fast Algorithm for Edge-Preserving Variational Multichannel Image Restoration , 2009, SIAM J. Imaging Sci..

[82]  Yin Zhang,et al.  User's Guide for YALL1: Your ALgorithms for L1 Optimization , 2009 .

[83]  Emmanuel J. Candès,et al.  NESTA: A Fast and Accurate First-Order Method for Sparse Recovery , 2009, SIAM J. Imaging Sci..