Compressive Sensing

[1]  Sören Bartels,et al.  Numerical Methods for Nonlinear Partial Differential Equations , 2015 .

[2]  Holger Rauhut,et al.  A Mathematical Introduction to Compressive Sensing , 2013, Applied and Numerical Harmonic Analysis.

[3]  S. Foucart A note on guaranteed sparse recovery via ℓ1-minimization , 2010 .

[4]  Jared Tanner,et al.  Phase Transitions for Greedy Sparse Approximation Algorithms , 2010, ArXiv.

[5]  Holger Rauhut,et al.  The Gelfand widths of lp-balls for 0p<=1 , 2010, J. Complex..

[6]  David P. Woodruff,et al.  Lower bounds for sparse recovery , 2010, SODA '10.

[7]  Massimo Fornasier,et al.  The application of joint sparsity and total variation minimization algorithms to a real-life art restoration problem , 2009, Adv. Comput. Math..

[8]  Carola-Bibiane Schönlieb,et al.  A convergent overlapping domain decomposition method for total variation minimization , 2009, Numerische Mathematik.

[9]  Thomas Strohmer,et al.  Compressed Remote Sensing of Sparse Objects , 2009, SIAM J. Imaging Sci..

[10]  Holger Rauhut,et al.  Compressive estimation of doubly selective channels: exploiting channel sparsity to improve spectral efficiency in multicarrier transmissions , 2009, ArXiv.

[11]  Holger Rauhut,et al.  Circulant and Toeplitz matrices in compressed sensing , 2009, ArXiv.

[12]  Justin K. Romberg,et al.  Beyond Nyquist: Efficient Sampling of Sparse Bandlimited Signals , 2009, IEEE Transactions on Information Theory.

[13]  Yaakov Tsaig,et al.  Fast Solution of $\ell _{1}$ -Norm Minimization Problems When the Solution May Be Sparse , 2008, IEEE Transactions on Information Theory.

[14]  M. Rudelson,et al.  On sparse reconstruction from Fourier and Gaussian measurements , 2008 .

[15]  Jan Vybíral,et al.  Widths of embeddings in function spaces , 2008, J. Complex..

[16]  R. DeVore,et al.  Compressed sensing and best k-term approximation , 2008 .

[17]  I. Daubechies,et al.  Iteratively reweighted least squares minimization for sparse recovery , 2008, 0807.0575.

[18]  Emmanuel J. Candès,et al.  Exact Matrix Completion via Convex Optimization , 2008, Found. Comput. Math..

[19]  Thomas Strohmer,et al.  Compressed sensing radar , 2008, 2008 IEEE International Conference on Acoustics, Speech and Signal Processing.

[20]  Mike E. Davies,et al.  Iterative Hard Thresholding for Compressed Sensing , 2008, ArXiv.

[21]  Pierre Vandergheynst,et al.  Dictionary Preconditioning for Greedy Algorithms , 2008, IEEE Transactions on Signal Processing.

[22]  Piotr Indyk,et al.  Combining geometry and combinatorics: A unified approach to sparse signal recovery , 2008, 2008 46th Annual Allerton Conference on Communication, Control, and Computing.

[23]  J. Romberg,et al.  Imaging via Compressive Sampling , 2008, IEEE Signal Processing Magazine.

[24]  E.J. Candes,et al.  An Introduction To Compressive Sampling , 2008, IEEE Signal Processing Magazine.

[25]  Deanna Needell,et al.  CoSaMP: Iterative signal recovery from incomplete and inaccurate samples , 2008, ArXiv.

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

[27]  Richard Baraniuk Compressive sensing , 2008, CISS.

[28]  Jean-Luc Starck,et al.  Compressed Sensing in Astronomy , 2008, IEEE Journal of Selected Topics in Signal Processing.

[29]  R. DeVore,et al.  A Simple Proof of the Restricted Isometry Property for Random Matrices , 2008 .

[30]  Massimo Fornasier,et al.  Restoration of Color Images by Vector Valued BV Functions and Variational Calculus , 2007, SIAM J. Appl. Math..

[31]  Holger Rauhut,et al.  Sparsity in Time-Frequency Representations , 2007, ArXiv.

[32]  Pablo A. Parrilo,et al.  Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization , 2007, SIAM Rev..

[33]  R. Vershynin,et al.  One sketch for all: fast algorithms for compressed sensing , 2007, STOC '07.

[34]  H. Rauhut Stability Results for Random Sampling of Sparse Trigonometric Polynomials , 2006, IEEE Transactions on Information Theory.

[35]  S. Mendelson,et al.  Uniform Uncertainty Principle for Bernoulli and Subgaussian Ensembles , 2006, math/0608665.

[36]  D. Donoho,et al.  Counting faces of randomly-projected polytopes when the projection radically lowers dimension , 2006, math/0607364.

[37]  D. Donoho For most large underdetermined systems of linear equations the minimal 𝓁1‐norm solution is also the sparsest solution , 2006 .

[38]  Graham Cormode,et al.  Combinatorial Algorithms for Compressed Sensing , 2006, 2006 40th Annual Conference on Information Sciences and Systems.

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

[40]  H. Rauhut Random Sampling of Sparse Trigonometric Polynomials , 2005, math/0512642.

[41]  Stephen P. Boyd,et al.  Convex Optimization , 2010, IEEE Transactions on Automatic Control.

[42]  E. Candès,et al.  Stable signal recovery from incomplete and inaccurate measurements , 2005, math/0503066.

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

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

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

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

[47]  H. Bungartz,et al.  Sparse grids , 2004, Acta Numerica.

[48]  R. Tibshirani,et al.  Least angle regression , 2004, math/0406456.

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

[50]  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.

[51]  Thomas Strohmer,et al.  GRASSMANNIAN FRAMES WITH APPLICATIONS TO CODING AND COMMUNICATION , 2003, math/0301135.

[52]  S. Muthukrishnan,et al.  Approximation of functions over redundant dictionaries using coherence , 2003, SODA '03.

[53]  O. Christensen An introduction to frames and Riesz bases , 2002 .

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

[55]  Sudipto Guha,et al.  Near-optimal sparse fourier representations via sampling , 2002, STOC '02.

[56]  Avi Wigderson,et al.  Randomness conductors and constant-degree lossless expanders , 2002, STOC '02.

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

[58]  Dimitris Achlioptas,et al.  Database-friendly random projections , 2001, PODS.

[59]  M. R. Osborne,et al.  A new approach to variable selection in least squares problems , 2000 .

[60]  M. R. Osborne,et al.  On the LASSO and its Dual , 2000 .

[61]  M. Unser Sampling-50 years after Shannon , 2000, Proceedings of the IEEE.

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

[63]  M. Talagrand Selecting a proportion of characters , 1998 .

[64]  Bhaskar D. Rao,et al.  Sparse signal reconstruction from limited data using FOCUSS: a re-weighted minimum norm algorithm , 1997, IEEE Trans. Signal Process..

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

[66]  Erich Novak,et al.  Optimal Recovery and n-Widths for Convex Classes of Functions , 1995 .

[67]  P. Schmieder,et al.  Application of nonlinear sampling schemes to COSY-type spectra , 1993, Journal of biomolecular NMR.

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

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

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

[71]  Rolf Schneider,et al.  Random projections of regular simplices , 1992, Discret. Comput. Geom..

[72]  Henryk Wozniakowski,et al.  Information-based complexity , 1987, Nature.

[73]  W. M. Carey,et al.  Digital spectral analysis: with applications , 1986 .

[74]  Charles R. Johnson,et al.  Matrix analysis , 1985 .

[75]  E. Gluskin NORMS OF RANDOM MATRICES AND WIDTHS OF FINITE-DIMENSIONAL SETS , 1984 .

[76]  B. S. Kašin,et al.  DIAMETERS OF SOME FINITE-DIMENSIONAL SETS AND CLASSES OF SMOOTH FUNCTIONS , 1977 .

[77]  A. Sterrett On the Detection of Defective Members of Large Populations , 1957 .

[78]  Holger Rauhut,et al.  The Gelfand widths of ℓp-balls for 0 , 2010, ArXiv.

[79]  Massimo Fornasier,et al.  Numerical Methods for Sparse Recovery , 2010 .

[80]  H. Rauhut Compressive Sensing and Structured Random Matrices , 2009 .

[81]  David L. Donoho,et al.  High-Dimensional Centrally Symmetric Polytopes with Neighborliness Proportional to Dimension , 2006, Discret. Comput. Geom..

[82]  E.J. Candes Compressive Sampling , 2022 .

[83]  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.

[84]  G. Lorentz,et al.  Constructive approximation : advanced problems , 1996 .

[85]  R. Tibshirani Regression Shrinkage and Selection via the Lasso , 1996 .

[86]  Yurii Nesterov,et al.  Interior-point polynomial algorithms in convex programming , 1994, Siam studies in applied mathematics.

[87]  J. Kuelbs Probability on Banach spaces , 1978 .

[88]  A. K. Cline Rate of Convergence of Lawson's Algorithm , 1972 .

[89]  Holger Rauhut,et al.  Edinburgh Research Explorer Identification of Matrices Having a Sparse Representation , 2022 .