~ Compressed Sensing

• 1. Tutorials
  • 1.1 Videos
    • ~ Compressed Sensing Videos: Where Is My Popcorn ? Summer School IMA 2007
    • ~ Compressed Sensing video presentations
  • 1.2 Presentations
    • Heavy hitters/sketching
      • ~ Compressed Sensing: Streaming School in Denmark Summer 2007
  • 1.3 Examples
    • ~ Compressed Sensing: How to wow your friends.
• 2. Short Reviews
  • ~ CS is not just Compressed Sampling nor Compressed Sensing.

    ~ Smashed filters and Bayesian approach to Compressed Sensing among others

    ~ Compressed Sensing: High Resolution Radar, Identification of Sparse Matrices

    ~ Compressed Sensing: Toeplitz, Radar, SAR, Bayesian Approach, Non Convex Minimization, Angle Preserving RIP

    ~ Compressed Sensing: Extending Reed-Solomon codes.

    ~ Compressed Sensing: stopping criterion, random multiscale projections, manifold learning, sparse image reconstruction

    ~ Compressed Sensing: Sensor Networks, Learning Compressed Sensing by Uncertain Compoent Analysis, Sparsity or Positivity ?, New CVX build

    ~ Compressed Sensing: Another deterministic code, a LASSO-CS root finder and a tree based greedy algorithm

    ~ Compressed Sensing: Neighborly polytopes, Acoustic Tomography, Sampling in union of linear subspaces, ROMP stability

    ~ Compressed Sensing: Sensor Networks, Learning Compressed Sensing by Uncertain Component Analysis, Sparsity or Positivity ?, New CVX build

• 3. Synthesis thoughts/ Theory
  • ~ Compressed Sensing: Random Thought on a Low Dimensional Embedding

    ~ Compressed Sensing: Reweighted L1 meets Europa

    On L1

    • ~ L1 — What is it good for ?
    • ~ The importance of L1
    • ~ Why L1 ?

    ~ Synthesis on Compressed Sensing and Dimensionality Reduction/ Imaging a Fractal Romanesco. July 17, 2007

    ~ It’s not about the sensor, it’s about the target

    ~ Compressed Sensing Illustrated

    ~ Why Compressed Sensing is important when detecting movement

    Random matrices

    • ~ Random Projection Lapack ?

    Greedy algorithms

    • ~ Compressed Sensing: It’s not just L1 anymore, greed can get you there too.

    ~ Amazing discoveries.

    3.2 Historical perspective

    • ~ Nothing short of a revolution, part 3 : It does not need to be nonlinear
    • ~ Nothing short of a revolution. Part deux: Pursuing a dream
    • ~ Nothing short of a revolution. Part I: When a scam can kill you
• 4. Hardware
  • 4.1 Rice Single Pixel Camera
    • ~ How does the Rice one pixel camera work ?
  • 4.2 My implementation
    • ~ Implementing Compressed Sensing in Applied Projects
    • Hyper-GeoCam
      • ~ Ready to launch
      • ~ HASP will launch today.
  • 4.3 Other Implementations
    • ~ Compressed Sensing Hardware Implementations

      ~ Compressed Sensing Hardware Implementations (part deux)

      ~ Compressed Sensing: Hardware Implementation, Part III, The explosive birth of coded aperture.

      ~ Compressed Sensing: Hardware Implementation, Part IV, Hyperspectral Coded Aperture, Connection between the CS camera and the primary visual cortex ?

      ~ Compressed Sensing: Single-Pixel Imaging via Compressive Sampling, Stable Manifold Embedding

  • 4.4 Disruptive Technology
    • ~ Compressed Sensing: Why does Rice Play Texas or How is CS a disruptive technology ? Part I
• 5. Algorithms
  • 5.1 Reconstruction Algorithm
    • ~ Compressed Sensing: Reweighted L1 and a nice summary on Compressed Sampling
    • ~ Compressed Sensing: Reweighted L1 meets Europa
    • ~ Compressed Sensing: Reweighted Lp through Least square (L2), Forget Europa, let’s shoot for Titan
    • ~ Compressed Sensing: SpaRSA and Image Registration using Random Projections
    • ~ Compressed Sensing: Solving the Basis Pursuit problem with a Bregman Iterative Algorithm
    • ~ Compressed Sensing: A new TwIST
  • 5.2 Measurement Algorithm
    • ~ Compressed Sensing: Algorithms for Deterministic Compressed Sensing
    • ~ Compressed Sensing: Random Undersampling in Geophysics and ROMP, a stable greedy algorithm
  • 5.3 Software Implementation
    • ~ SPGL1: a solver for large-scale sparse reconstruction problems
    • ~ Tree based pursuit
    • ~ Sparsify, another reason you should not avoid Compressed Sensing
    • ~ There are now three Compressed Sensing Reconstruction Codes available
    • ~ l1_ls: Simple Matlab Solver for l1-regularized Least Squares Problems (compressed sensing)
    • Bayesian approach
      • ~ Bayesian Compressive Sensing and other items.
    • ~ Compressed Sensing: Chaining Pursuit Code for dimension reduction in the L1 norm for sparse vectors
    • ~ Compressed Sensing: Sparco helps you test all these spiffy reconstruction algorithms
    • ~ Monday Morning Algorithm Part deux: Reweighted Lp for Non-convex Compressed Sensing Reconstruction
    • ~ Compressed Sensing: Sparse PCA and a Compressed Sensing Search Engine
    • ~ Compressed Sensing: Restricted Isometry Properties and Nonconvex Compressive Sensing
    • ~ Compressed Sensing: SpaRSA and Image Registration using Random Projections
  • 5.4 Monday Morning Algorithm
    • ~ Monday Morning Algorithm Part 3: Compressed Sensing meets Machine Learning / Recognition via Sparse Representation Classification Algorithm
• 6. Applications
  • 6.1 Brain / Cognition
    • ~ Compressed Sensing in the Primary Visual Cortex ?
    • ~ Compressed Sensing, Primary Visual Cortex, Dimensionality Reduction, Manifolds and Autism
  • 6.2 Machine Learning
    • ~ Machine Learning and Compressed Sensing
    • ~ Compressed Sensing: RandomFaces prove that faces lie in a low dimensional manifold
  • 6.3 Solving integral equations
    • ~ Finite Rate of Innovation is the reason why S_n works in Neutron Transport ?
    • ~ Compressive Sensing as a way to solve Integral Equations ?
    • ~ Compressive Sensing Radiation Detector
    • ~ Approaching a Random Radiation Detector
  • 6.4 SAR
    • ~ Adding Search and Rescue Capabilities (part I): Using Hyperspectral and Multispectral Cameras to Search for Non-Evading Targets
  • 6.5 Other
    • ~ Compressed Sensing: Universal Dimensionality Reduction, Pattern Matching and a Biology Inspired Faster Reconstruction Algorithm

      ~ Sparse Representations and High Dimensional Geometry: The upcoming success of randomized algorithms

      ~ Deep down, Making sense of it all one bit at a time

• 7. Reference Material
  • ~ Rice Compressed Sensing Site Update.
  • ~ Compressed Sensing: Blog entries and website updates.
• 8. Miscelaneous
  • ~ Traduction de Compressed Sensing en Francais
  • ~ Compressed Sensing: Map of entries from this blog
  • ~ Monday Morning Algorithm Part 1: Fast Low Rank Approximation using Random Projections
  • ~ Trace: What is it good for ? – How Compressed Sensing relates to Dimensionality Reduction
  • ~ Sparsity: What is it good for ?

Tutorials

• Emmanuel Candès, Compressive sampling. (Int. Congress of Mathematics, 3, pp. 1433-1452, Madrid, Spain, 2006)
• Richard Baraniuk, Compressive Sensing. (IEEE Signal Processing Magazine, July 2007)
• Marco Duarte, Mark Davenport, Dharmpal Takhar, Jason Laska, Ting Sun, Kevin Kelly, and Richard Baraniuk, Single-pixel imaging via compressive sampling. (To appear in IEEE Signal Processing Magazine)

Compressive Sensing

• Emmanuel Candès, Justin Romberg, and Terence Tao, Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information. (IEEE Trans. on Information Theory, 52(2) pp. 489 – 509, February 2006)
• Emmanuel Candès and Justin Romberg, Quantitative robust uncertainty principles and optimally sparse decompositions. (Foundations of Comput. Math., 6(2), pp. 227 – 254, April 2006)
• David Donoho, Compressed sensing. (IEEE Trans. on Information Theory, 52(4), pp. 1289 – 1306, April 2006)
• Emmanuel Candès and Terence Tao, Near optimal signal recovery from random projections: Universal encoding strategies? (IEEE Trans. on Information Theory, 52(12), pp. 5406 – 5425, December 2006)
• Emmanuel Candès and Justin Romberg, Practical signal recovery from random projections. (Preprint, Jan. 2005)
• David Donoho and Yaakov Tsaig, Extensions of compressed sensing. (Signal Processing, 86(3), pp. 533-548, March 2006)
• Emmanuel Candès, Justin Romberg, and Terence Tao, Stable signal recovery from incomplete and inaccurate measurements. (Communications on Pure and Applied Mathematics, 59(8), pp. 1207-1223, August 2006)
• Jarvis Haupt and Rob Nowak, Signal reconstruction from noisy random projections. (IEEE Trans. on Information Theory, 52(9), pp. 4036-4048, September 2006)
• Emmanuel Candès and Terence Tao, The Dantzig Selector: Statistical estimation when p is much larger than n (To appear in Annals of Statistics)
• Richard Baraniuk, Mark Davenport, Ronald DeVore, and Michael Wakin, A simple proof of the restricted isometry property for random matrices. (To appear in Constructive Approximation) [Formerly titled "The Johnson-Lindenstrauss lemma meets compressed sensing"]
• Albert Cohen, Wolfgang Dahmen, and Ronald DeVore, Compressed sensing and best k-term approximation. (Preprint, 2006) [Formerly titled "Remarks on compressed sensing"]
• Martin J. Wainwright, Sharp thresholds for high-dimensional and noisy recovery of sparsity (Proc. Allerton Conference on Communication, Control, and Computing, Monticello, IL, September 2006)
• Holger Rauhut, Karin Schass, and Pierre Vandergheynst, Compressed sensing and redundant dictionaries. (Preprint, 2006)
• Emmanuel Candès and Justin Romberg, Sparsity and incoherence in compressive sampling. (Inverse Problems, 23(3) pp. 969-985, 2007)
• Ronald A. DeVore, Deterministic constructions of compressed sensing matrices. (Preprint, 2007)
• Piotr Indyk, Explicit constructions for compressed sensing of sparse signals. (Symp. on Discrete Algorithms, 2008)
• Yin Zhang, A simple proof for recoverability of ell-1-minimization: go over or under? (Preprint, 2005)
• Yin Zhang, A simple proof for recoverability of ell-1-minimization (II): the nonnegative case. (Preprint, 2005)
• Yin Zhang, When is missing data recoverable? (Preprint, 2006)
• Boris S. Kashin and Vladimir N. Temlyakov, A remark on compressed sensing. (Preprint, 2007)
• Waheed Bajwa, Jarvis Haupt, Gil Raz, Stephen Wright, and Robert Nowak, Toeplitz-structured compressed sensing matrices. (IEEE Workshop on Statistical Signal Processing (SSP), Madison, Wisconsin, August 2007)
• Weiyu Xu and Babak Hassibi, Efficient compressive sensing with determinstic guarantees using expander graphs. (IEEE Information Theory Workshop, Lake Tahoe, September 2007)
• Yoav Sharon, John Wright, and Yi Ma, Computation and relaxation of conditions for equivalence between ell-1 and ell-0 minimization. (Preprint, 2007)
• Thong T. Ho, Trac D. Tran, and Lu Gan, Fast compressive sampling with structurally random matrices. (Preprint, 2007)

Extensions of Compressive Sensing

• Gabriel Peyré, Best basis compressed sensing. (Preprint, 2006) [See also related conference publication: NeuroComp 2006]
• Michael Elad, Optimized projections for compressed sensing. (Preprint, 2006)
• Yue Lu and Minh Do, A theory for sampling signals from a union of subspaces. (Preprint, 2007)
• Lawrence Carin, Dehong Liu, and Ya Xue, In Situ Compressive Sensing. (Preprint, 2007) [See also related conference publication: SSP 2007]
• Remi Gribonval and Morten Nielsen, Beyond sparsity : recovering structured representations by ell-1-minimization and greedy algorithms – Application to the analysis of sparse underdetermined ICA. (To appear in Advances in Computational Mathematics)
• Cynthia Dwork, Frank McSherry, and Kunal Talwar, The price of privacy and the limits of LP decoding. (Symp. on Theory of Computing (STOC), San Diego, California, June, 2007)
• Akram Aldroubi, Carlos Cabrelli, and Ursula Molter, Optimal non-linear models for sparsity and sampling. (Preprint, 2007)
• Lawrence Carin, Dehong Liu, Wenbin Lin, and Bin Guo, Compressive sensing for multi-static scattering analysis. (Preprint, 2007)
• Benjamin Rect, Maryam Fazel, and Pablo A. Parrilo, Guaranteed minimum-rank solution of linear matrix equations via nuclear norm minimization. (Preprint, 2007)
• Mona Sheikh and Richard Baraniuk, Blind error-free detection of transform-domain watermarks. (IEEE Int. Conf. on Image Processing (ICIP), San Antonio, Texas, September 2007)
• Gotz Pfander, Holger Rauhut, and Jared Tanner, Identification of matrices having a sparse representation. (Preprint, 2007) [See also related note]
• Gotz Pfander and Holger Rauhut, Sparsity in time-frequency representations. (Preprint, 2007)
• Alfred M. Bruckstein, Michael Elad, and Michael Zibulevsky, A non-negative and sparse enough solution of an underdetermined linear system of equations is unique. (Preprint, 2007)
• Thomas Blumensath and Mike E. Davies, Sampling theorems for signals from the union of linear subspaces. (Preprint, 2007)
• Rick Chartrand and Valentina Staneva, Restricted isometry properties and nonconvex compressive sensing. (Preprint, 2007)

Multi-Sensor and Distributed Compressive Sensing

• Dror Baron, Michael Wakin, Marco Duarte, Shriram Sarvotham, and Richard Baraniuk, Distributed compressed sensing. (Preprint, 2005) [See also related technical report and conference publications: Allerton 2005, Asilomar 2005, NIPS 2005, IPSN 2006]
• Waheed Bajwa, Jarvis Haupt, Akbar Sayeed, and Rob Nowak, Compressive wireless sensing. (Int. Conf. on Information Processing in Sensor Networks (IPSN), Nashville, Tennessee, April 2006)
• Michael Rabbat, Jarvis Haupt, Aarti Singh, and Rob Nowak, Decentralized compression and predistribution via randomized gossiping. (Int. Conf. on Information Processing in Sensor Networks (IPSN), Nashville, Tennessee, April 2006)
• Massimo Fornasier and Holger Rauhut, Recovery algorithms for vector valued data with joint sparsity constraints. (Preprint, 2006)
• Rémi Gribonval, Holger Rauhut, Karin Schnass, and Pierre Vandergheynst, Atoms of all channels, unite! Average case analysis of multi-channel sparse recovery using greedy algorithms. (Preprint, 2007) [See also related conference publication: ICASSP 2007]
• Wei Wang, Minos Garofalakis, and Kannan Ramchandran, Distributed sparse random projections for refinable approximation. (Int. Conf. on Information Processing in Sensor Networks (IPSN), Cambridge, Massachusetts, April 2007)
• W. Bajwa, J. Haupt, A. Sayeed and R. Nowak, Joint source-channel communication for distributed estimation in sensor networks. (IEEE Trans. on Information Theory, 53(10) pp. 3629-3653, October 2007)
• Shuchin Aeron, Manqi Zhao, and Venkatesh Saligrama, Sensing capacity of sensor networks: Fundamental tradeoffs of SNR, sparsity, and sensing diversity. (Information Theory and Applications Workshop, January 2007)
• Shuchin Aeron, Manqi Zhao, and Venkatesh Saligrama, On sensing capacity of sensor networks for the class of linear observation, fixed SNR models. (Preprint, 2007)

Compressive Sensing Recovery Algorithms

• Joel Tropp and Anna Gilbert, Signal recovery from partial information via orthogonal matching pursuit. (Preprint, 2005)
• Marco Duarte, Michael Wakin, and Richard Baraniuk, Fast reconstruction of piecewise smooth signals from random projections. (SPARS Workshop, November 2005)
• Chinh La and Minh Do, Signal reconstruction using sparse tree representations. (SPIE Wavelets XI, San Diego, California, September 2005)
• Shriram Sarvotham, Dror Baron, and Richard Baraniuk, Sudocodes – Fast measurement and reconstruction of sparse signals. (IEEE Int. Symposium on Information Theory (ISIT), Seattle, Washington, July 2006)
• Shriram Sarvotham, Dror Baron, and Richard Baraniuk, Compressed sensing reconstruction via belief propagation. (Preprint, 2006)
• David Donoho and Yaakov Tsaig, Fast solution of ell-1-norm minimization problems when the solution may be sparse. (Preprint, 2006)
• Massimo Fornasier and Holger Rauhut, Iterative thresholding algorithms. (Preprint, 2007)
• Rick Chartrand, Exact reconstructions of sparse signals via nonconvex minimization. (IEEE Signal Proc. Lett., 14(10) pp. 707-710, 2007)
• Mário A. T. Figueiredo, Robert D. Nowak, and Stephen J. Wright, Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems. (To appear in IEEE Journal of Selected Topics in Signal Processing, 2007)
• Seung-Jean Kim, Kwangmoo Koh, Michael Lustig, Stephen Boyd, and Dimitry Gorinevsky, A method for large-scale ell-1-regularized least squares problems with applications in signal processing and statistics. (Preprint, 2007)
• Thomas Blumensath and Mike E. Davies, Iterative thresholding for sparse approximations. (Preprint, 2007)
• Thomas Blumensath and Mike E. Davies, Gradient pursuits. (Preprint, 2007)
• Karen Egiazarian, Alessandro Foi, and Vladimir Katkovnik, Compressed sensing image reconstruction via recursive spatially adaptive filtering. (Preprint, 2007)
• Ingrid Daubechies, Massimo Fornasier, and Ignace Loris, Accelerated projected gradient method for linear inverse problems with sparsity constraints. (Preprint, 2007)
• Massimo Fornasier, Domain decomposition methods for linear inverse problems with sparsity constraints. (Preprint, 2007)
• Ewout van den Berg and Michael Friedlander, In pursuit of a root. (Preprint, 2007)
• Deanna Needell and Roman Vershynin, Uniform uncertainty principle and signal recovery via regularized orthogonal matching pursuit. (Preprint, 2007)
• Kristan Bredies and Dirk A. Lorenz, Iterated hard shrinkage for minimization problems with sparsity constraints. (Preprint, 2007)
• José Bioucas-Dias and Mário Figueiredo, A new TwIST: two-step iterative shrinkage/thresholding algorithms for image restoration. (Preprint, 2007)
• Mark Iwen, A deterministic sub-linear time sparse Fourier algorithm via non-adaptive compressed sensing methods. (Preprint, 2007)
• Elaine T. Hale, Wotao Yin, and Yin Zhang, A fixed-point continuation method for ell-1 regularized minimization with applications to compressed sensing. (Preprint, 2007)
• Petros Boufounos, Marco F. Duarte, and Richard G. Baraniuk, Sparse signal reconstruction from noisy compressive measurements using cross validation. (Proc. IEEE Workshop on Statistical Signal Processing, Madison, Wisconsin, August 2007)
• Wotao Yin, Stanley Osher, Donald Goldfarm, and Jerome Darbon, Bregman iterative algorithms for ell-1 minimization with applications to compressed sensing. (Preprint, 2007)
• Roland Griesse, Dirk A. Lorenz, A semismooth Newton method for Tikhonov functionals with sparsity constraints. (Preprint, 2007)
• Emmanuel Candès, Michael Wakin, and Stephen Boyd, Enhancing sparsity by reweighted ell-1 minimization. (Preprint, 2007)
• Rick Chartrand and Wotao Yin, Iteratively reweighted algorithms for compressive sensing. (Preprint, 2007)
• Petros Boufounos, Marco Duarte, and Richard Baraniuk, Sparse signal reconstruction from noisy compressive measurements using cross validation. (IEEE Workshop on Statistical Signal Processing (SSP), Madison, Wisconsin, August 2007)
• Sadegh Jokar and Marc E. Pfetsch, Exact and approximate sparse solutions of underdetermined linear equations. (Preprint, 2007)
• Deanna Needell and Roman Vershynin, Signal recovery from incomplete and inaccurate measurements via regularized orthogonal matching pursuit. (Preprint, 2007)
• Nam H. Nguyen and Trac D. Tran, The stability of regularized orthogonal mathcing pursuit. (Preprint, 2007)

Foundations and Connections

Coding and Information Theory

• Emmanuel Candès and Terence Tao, Decoding by linear programming. (IEEE Trans. on Information Theory, 51(12), pp. 4203 – 4215, December 2005)
• Emmanuel Candès and Terence Tao, Error correction via linear programming. (Preprint, 2005)
• Mark Rudelson and Roman Vershynin, Geometric approach to error correcting codes and reconstruction of signals. (Int. Mathematical Research Notices, 64, pp. 4019 – 4041, 2005)
• Emmanuel Candès and Justin Romberg, Encoding the ell-p ball from limited measurements. (IEEE Data Compression Conference (DCC), Snowbird, UT, 2006)
• Shriram Sarvotham, Dror Baron, and Richard Baraniuk, Measurements vs. bits: Compressed sensing meets information theory. (Allerton Conference on Communication, Control, and Computing, Monticello, IL, September 2006)
• Emmanuel Candès and Paige Randall, Highly robust error correction by convex programming. (Preprint, 2006)
• Petros Boufounos and Richard Baraniuk, Quantization of sparse representations. (Rice ECE Department Technical Report TREE 0701 – Summary appears in Data Compression Conference (DCC), Snowbird, Utah, March 2007)
• Martin Wainwright, Information-theoretic bounds on sparsity recovery in the high-dimensional and noisy setting. (IEEE Int. Symposium on Information Theory (ISIT), Nice, France, June 2007)
• Rick Chartrand, Nonconvex compressed sensing and error correction. (IEEE Int. Conf. on Acoustics, Speech, and Signal Processing (ICASSP), Honolulu, Hawaii, April 2007)

High-Dimensional Geometry

• David Donoho, High-dimensional centrally-symmetric polytopes with neighborliness proportional to dimension. (Disc. Comput. Geometry, 35(4) pp. 617-652, 2006)
• David Donoho, Neighborly polytopes and sparse solutions of undetermined linear equations. (Preprint, 2005)
• David Donoho and Jared Tanner, Neighborliness of randomly-projected simplices in high dimensions. (Proc. National Academy of Sciences, 102(27), pp. 9452-9457, 2005)
• David Donoho and Jared Tanner, Counting faces of randomly-projected polytopes when the projection radically lowers dimension. (Submitted to Journal of the AMS)
• Richard Baraniuk and Michael Wakin, Random projections of smooth manifolds. (To appear in Foundations of Computational Mathematics) [See also related conference publication: ICASSP 2006]
• Venkatesan Guruswami, James R. Lee, and Alexander Razborov, Almost Euclidean subspaces of ell-1-N via expander codes. (Electronic Colloquium on Computational Complexity, Report TR07-089, September, 2007)

Ell-1 Norm Minimization

• David Donoho, For most large underdetermined systems of linear equations, the minimal ell-1 norm solution is also the sparsest solution. (Communications on Pure and Applied Mathematics, 59(6), pp. 797-829, June 2006)
• David Donoho, For most large underdetermined systems of linear equations, the minimal ell-1 norm near-solution approximates the sparsest near-solution. (Communications on Pure and Applied Mathematics, 59(7), pp. 907-934, July 2006)
• David Donoho and Jared Tanner, Sparse nonnegative solutions of underdetermined linear equations by linear programming. (Proc. National Academy of Sciences, 102(27), pp.9446-9451, 2005)
• David Donoho and Jared Tanner, Thresholds for the recovery of sparse solutions via ell-1 minimization. (Conf. on Information Sciences and Systems, March 2006)
• Rémi Gribonval and Morten Nielsen, Highly sparse representations from dictionaries are unique and independent of the sparseness measure. (Applied and Computational Harmonic Analysis, 22(3), pp. 335-355, May 2007) [See also related conference publication: ICA 2004]
• Rémi Gribonval, Rosa Maria Figueras I Ventura, and Pierre Vandergheynst, A simple test to check the optimality of a sparse signal approximation. (EURASIP Signal Processing, special issue on Sparse Approximations in Signal and Image Processing, 86(3), pp. 496-510, March 2006) [See also related conference publication: ICASSP 2005]

Statistical Signal Processing

• Marco Duarte, Mark Davenport, Michael Wakin, and Richard Baraniuk, Sparse signal detection from incoherent projections. (IEEE Int. Conf. on Acoustics, Speech, and Signal Processing (ICASSP), Toulouse, France, May 2006)
• Mark Davenport, Michael Wakin, and Richard Baraniuk, Detection and estimation with compressive measurements. (Rice ECE Department Technical Report TREE 0610, November 2006)
• Jarvis Haupt, Rui Castro, Robert Nowak, Gerald Fudge, and Alex Yeh, Compressive sampling for signal classification. (Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, California, October 2006)
• Mark Davenport, Marco Duarte, Michael Wakin, Jason Laska, Dharmpal Takhar, Kevin Kelly, and Richard Baraniuk, The smashed filter for compressive classification and target recognition. (Computational Imaging V at SPIE Electronic Imaging, San Jose, California, January 2007)
• Jarvis Haupt and Robert Nowak, Compressive sampling for signal detection. (IEEE Int. Conf. on Acoustics, Speech, and Signal Processing (ICASSP), Honolulu, Hawaii, April 2007)
• Frank Boyle, Jarvis Haupt, Gerald Fudge, and Robert Nowak, Detecting signal structure from randomly-sampled data. (IEEE Workshop on Statistical Signal Processing (SSP), Madison, Wisconsin, August 2007)
• Marco Duarte, Mark Davenport, Michael Wakin, Jason Laska, Dharmpal Takhar, Kevin Kelly, and Richard Baraniuk, Multiscale random projections for compressive classification. (IEEE Conf. on Image Processing (ICIP), San Antonio, Texas, September 2007)

Machine Learning

• John Wright, Arvind Ganesh, Allen Yang, and Yi Ma, Robust face recognition via sparse representation. (Preprint, 2007)
• Allen Yang, John Wright, Yi Ma, and Shankar Sastry, Feature selection in face recognition: A sparse representation perspective. (Preprint, 2007)
• Chinmay Hegde, Michael Wakin, and Richard Baraniuk, Random projections for manifold learning. (Neural Information Processing Systems (NIPS), Vancouver, Canada, December 2007) [See also related technical report]

Bayesian Methods

• Mauricio Sacchi, Tadeusz Ulrych, and Colin Walker, Interpolation and extrapolation using a high-resolution discrete Fourier transform. (IEEE Trans. on Signal Processing, 46(1) pp. 31 – 38, January 1998)
• Shihao Ji, Ya Xue, and Lawrence Carin, Bayesian compressive sensing. (Preprint, 2007) [See also related conference publication: ICML 2007]
• David Wipf, Jason Palmer, Bhaskar Rao, and Kenneth Kreutz-Delgado, Performance evaluation of latent variable models with sparse priors. (IEEE Int. Conf. on Acoustics, Speech, and Signal Processing (ICASSP), Honolulu, Hawaii, May 2007)
• Shihao Ji, David Dunson, and Lawrence Carin, Multi-task compressive sensing. (Preprint, 2007)

Finite Rate of Innovation

• Martin Vetterli, Pina Marziliano, and Thierry Blu, Sampling signals with finite rate of innovation. (IEEE Trans. on Signal Processing, 50(6), pp. 1417-1428, June 2002)
• Irena Maravic and Martin Vetterli, Sampling and reconstruction of signals with finite rate of innovation in the presence of noise. (IEEE Trans. on Signal Processing, 53(8), pp. 2788-2805, August 2005)
• Yue Lu and Minh Do, A geometrical approach to sampling signals with finite rate of innovation. (IEEE Int. Conf. on Acoustics, Speech, and Signal Processing (ICASSP), Montreal, Canada, May 2004)
• Ivana Jovanovic and Baltasar Beferull-Lozano, Oversampled A/D conversion and error-rate dependence of nonbandlimited signals with finite rate of innovation. (IEEE Trans. on Signal Processing, 54(6), pp. 2140-2154 , June 2006)
• Pier Luigi Dragotti, Martin Vetterli, and Thierry Blu, Sampling moments and reconstructing signals of finite rate of innovation: Shannon meets Strang-Fix. (IEEE Trans. on Signal Processing, 55(7), pp. 1741-1757, May 2007)
• P. Shukla and P. L. Dragotti, Sampling schemes for multidimensional signals with finite rate of innovation. (IEEE Trans. on Signal Processing, 55(7), pp. 3670-3686, July 2007)

Multi-band Signals

• Moshe Mishali and Yonina C. Eldar, Blind multi-band signal reconstruction: compressed sensing for analog signals. (Preprint, 2007)

Data Stream Algorithms

Heavy-Hitters

• Graham Cormode and S. Muthukrishnan, Towards an algorithmic theory of compressed sensing. (Technical Peport DIMACS TR 2005-25, 2005)
• Graham Cormode and S. Muthukrishnan, Combinatorial algorithms for compressed sensing. (Technical Report DIMACS TR 2005-40, 2005)
• S. Muthukrishnan, Some algorithmic problems and results in compressed sensing. (Preprint, 2006)
• Anna Gilbert, Martin Strauss, Joel Tropp, and Roman Vershynin, One sketch for all: Fast algorithms for compressed sensing. (Symp. on Theory of Computing (STOC), San Diego, California, June, 2007)

Random Sampling

• Anna Gilbert, Sudipto Guha, Piotr Indyk, S. Muthukrishnan, and Martin Strauss, Near-optimal sparse Fourier representations via sampling. (ACM Symposium on Theory of Computing (STOC), 2002)
• Anna Gilbert, S. Muthukrishnan, and M. Strauss, Improved time bounds for near-optimal sparse Fourier representation via sampling. (SPIE Wavelets XI, San Diego, California, September 2005)
• Holger Rauhut, Random sampling of sparse trigonometric polynomials. (Applied and Computational Harmonic Analysis, 22(1), pp. 16-42, Jan. 2007)
• Stefan Kunis and Holger Rauhut, Random sampling of sparse trigonometric polynomials II – Orthogonal matching pursuit versus basis pursuit. (Preprint, 2006)
• Holger Rauhut, Stability results for random sampling of sparse trigonometric polynomials. (Preprint, 2006)

Histogram Maintenance

• Nitin Thaper, Sudipto Guha, Piotr Indyk, and Nick Koudas, Dynamic multidimensional histograms. (SIGMOD 2002, Madison, Wisconson, June 2002)
• Anna Gilbert, Sudipto Guha, Piotr Indyk, Yannis Kotidis, S. Muthukrishnan, and Martin J. Strauss, Fast small-space algorithms for approximate histogram maintenance. (Symp. on Theory of Computing (STOC), Montréal, Canada, May 2002)

Dimension Reduction and Embeddings

• Anna Gilbert, Martin Strauss, Joel Tropp, and Roman Vershynin, Sublinear, Small-space approximation of compressible signals and uniform algorithmic embeddings. (Preprint, 2005) [See Vershynin's discussion of this paper here]
• Anna Gilbert, Martin Strauss, Joel Tropp, and Roman Vershynin, Algorithmic linear dimension reduction in the ell-1 norm for sparse vectors. (Preprint, 2006) [See also related conference publication: Allerton 2006]

Applications of Compressive Sensing

Compressive Imaging

• Michael Wakin, Jason Laska, Marco Duarte, Dror Baron, Shriram Sarvotham, Dharmpal Takhar, Kevin Kelly, and Richard Baraniuk, An architecture for compressive imaging. (Int. Conf. on Image Processing (ICIP), Atlanta, Georgia, October 2006)
• Michael Wakin, Jason Laska, Marco Duarte, Dror Baron, Shriram Sarvotham, Dharmpal Takhar, Kevin Kelly, and Richard Baraniuk, Compressive imaging for video representation and coding. (Proc. Picture Coding Symposium (PCS), Beijing, China, April 2006)
• Dharmpal Takhar, Jason Laska, Michael Wakin, Marco Duarte, Dror Baron, Shriram Sarvotham, Kevin Kelly, and Richard Baraniuk, A new compressive imaging camera architecture using optical-domain compression. (Computational Imaging IV at SPIE Electronic Imaging, San Jose, California, January 2006)
• Lu Gan, Block compressed sensing of natural images. (Conf. on Digital Signal Processing (DSP), Cardiff, UK, July 2007)
• Ray Maleh and Anna Gilbert, Multichannel image estimation via simultaneous orthogonal matching pursuit. (IEEE Workshop on Statistical Signal Processing (SSP), Madison, Wisconsin, August 2007)
• Ray Maleh, Anna Gilbert, and Martin Strauss, Sparse gradient image reconstruction done faster. (IEEE Conf. on Image Processing (ICIP), San Antonio, Texas, September 2007)
• Karen Egiazarian, Alessandro Foi, and Vladimir Katkovnik, Compressed sensing image reconstruction via recursive spatially adaptive filtering. (IEEE Conf. on Image Processing (ICIP), San Antonio, Texas, September 2007)

Medical Imaging

• Michael Lustig, David Donoho, and John M. Pauly, Sparse MRI: The application of compressed sensing for rapid MR imaging. (Magnetic Resonance in Medicine, 58(6) pp. 1182 – 1195, December 2007) [See also related conference publication: ISMRM 2006, SPARS 2005, ISMRM 2005]
• M. Lustig, J. M. Santos, D. L. Donoho, and J. M. Pauly, k-t SPARSE: High frame rate dynamic MRI exploiting spatio-temporal sparsity (ISMRM, Seattle, Washington, May 2006)
• Hong Jung, Jong Chul Ye, and Eung Yeop Kim, Improved k-t BLASK and k-t SENSE using FOCUSS (Phys. Med. Biol., 52 pp. 3201 – 3226, 2007)
• Jong Chul Ye, Compressed sensing shape estimation of star-shaped objects in Fourier imaging (Preprint, 2007)
• Joshua Trzasko, Armando Manduca, and Eric Borisch, Highly undersampled magnetic resonance image reconstruction via homotopic ell-0-minimization (Preprint, 2007) [See also related conference publication: SSP 2007]

Analog-to-Information Conversion

• Joel Tropp, Michael Wakin, Marco Duarte, Dror Baron, and Richard Baraniuk, Random filters for compressive sampling and reconstruction. (IEEE Int. Conf. on Acoustics, Speech, and Signal Processing (ICASSP), Toulouse, France, May 2006)
• Sami Kirolos, Jason Laska, Michael Wakin, Marco Duarte, Dror Baron, Tamer Ragheb, Yehia Massoud, and Richard Baraniuk, Analog-to-information conversion via random demodulation. (IEEE Dallas Circuits and Systems Workshop (DCAS), Dallas, Texas, 2006)
• Jason Laska, Sami Kirolos, Yehia Massoud, Richard Baraniuk, Anna Gilbert, Mark Iwen, and Martin Strauss, Random sampling for analog-to-information conversion of wideband signals. (IEEE Dallas Circuits and Systems Workshop (DCAS), Dallas, Texas, 2006)
• Jason Laska, Sami Kirolos, Marco Duarte, Tamer Ragheb, Richard Baraniuk, and Yehia Massoud, Theory and implementation of an analog-to-information converter using random demodulation. (IEEE Int. Symp. on Circuits and Systems (ISCAS), New Orleans, Louisiana, 2007)
• Tamer Ragheb, Sami Kirolos, Jason Laska, Anna Gilbert, Martin Strauss, Richard Baraniuk, and Yehia Massoud, Implementation models for analog-to-information conversion via random sampling. (Midwest Symposium on Circuits and Systems (MWSCAS), 2007)
• Petros Boufounos and Richard G. Baraniuk, Sigma delta quantization for compressive sensing. (Preprint, 2007)

Biosensing

• Mona Sheikh, Olgica Milenkovic, and Richard Baraniuk, Compressed sensing DNA microarrays. (Rice ECE Department Technical Report TREE 0706, May 2007)
• Mona Sheikh, Shriram Sarvotham, Olgica Milenkovic, and Richard Baraniuk, DNA array decoding from nonlinear measurements by beleif propagation. (IEEE Workshop on Statistical Signal Processing (SSP), Madison, Wisconsin, August 2007)
• Mona Sheikh, Olgica Milenkovic, and Richard Baraniuk, Designing compressive sensing DNA microarrays. (IEEE Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP), St. Thomas, U.S. Virgin Islands, December 2007)

Geophysical Data Analysis

• Tim Lin and Felix. J. Herrmann, Compressed wavefield extrapolation. (To appear in Geophysics, 2007) [See also related conference publication: SEG 2007]
• Felix J. Herrmann, Deli Wang, Gilles Hennenfent and Peyman Moghaddam, Curvelet-based seismic data processing: a multiscale and nonlinear approach. (To appear in Geophysics, 2007)
• Felix J. Herrmann and Gilles Hennenfent, Non-parametric seismic data recovery with curvelet frames. (UBC Earth & Ocean Sciences Department Technical Report TR-2007-1, 2007)
• Gilles Hennenfent and Felix J. Herrmann, Curvelet reconstruction with sparsity-promoting inversion: successes and challenges. (EAGE 2007)
• Gilles Hennenfent and Felix J. Herrmann, Irregular sampling: from aliasing to noise. (EAGE 2007)
• Felix J. Herrmann, Deli Wang, and Gilles Hennenfent, Multiple prediction from incomplete data with the focused curvelet transform. (SEG 2007)
• Challa Sastry, Gilles Hennenfent, and Felix J. Herrmann, Signal reconstruction from incomplete and misplaced measurements. (EAGE 2007)
• Felix J. Herrmann, Surface related multiple prediction from incomplete data. (EAGE 2007)
• Gilles Hennenfent and Felix J. Herrmann, Simply denoise: wavefield reconstruction via jittered undersampling. (Geophysics, 2008)

Hyperspectral Imaging

• Rebecca Willett, Michael Gehm, and David Brady, Multiscale reconstruction for computational spectral imaging. (Computational Imaging V at SPIE Electronic Imaging, San Jose, California, January 2007)

Compressive Radar

• Richard Baraniuk and Philippe Steeghs, Compressive radar imaging. (IEEE Radar Conference, Waltham, Massachusetts, April 2007)
• Sujit Bhattacharya, Thomas Blumensath, Bernard Mulgrew, and Mike Davies, Fast encoding of synthetic aperture radar raw data using compressed sensing. (IEEE Workshop on Statistical Signal Processing, Madison, Wisconsin, August 2007)
• Matthew Herman and Thomas Strohmer, High-resolution radar via compressed sensing. (Preprint, 2007)

Software

• l1-Magic
• SparseLab
• GPSR
• ell-1 LS: Simple Matlab Solver for ell-1-Regularized Least Squares Problems
• sparsify
• MPTK: Matching Pursuit Toolkit [See also related conference publication: ICASSP 2006]
• Bayesian Compressive Sensing
• SPGL1: A solver for large scale sparse reconstruction
• sparseMRI
• FPC
• Chaining Pursuit
• Regularized OMP
• SPARCO: A toolbox for testing sparse reconstruction algorithms [See also related technical report]
• TwIST

Links

Conferences and Workshops

• IEEE International Conference on Acoustics, Speech, and Signal Processing (April, 2008)
• IEEE Statistical Signal Processing Workshop (August, 2007)
• MADALGO Summer School on Data Stream Algorithms (August, 2007)
• 2007 von Neumann Symposium on Sparse Representations and High-Dimensional Geometry (July, 2007)
• IMA New Directions Short Course: Compressive Sampling and Frontiers in Signal Processing (June, 2007)
• IPAM Short Course on Sparse Representations and High-Dimensional Geometry (June, 2007)
• IEEE International Conference on Acoustics, Speech, and Signal Processing (April, 2007)
• IITK Data Streams Workshop (December, 2006)
• Sparse Approximation Workshop (November, 2006)
• Signal Processing with Adaptative Sparse Structured Representations (November, 2005)
• Dagstuhl Workshop on Sublinear Algorithms (July, 2005)

Blogs

• Nuit Blanche
• Geomblog
• What’s new?

Other Related Links

• Preprints in sparse recovery / Summary of properties of random matrices
• Resources on Geophysical Data Reconstruction and Inversion using Sparsity Norms