Sparco: A Testing Framework for Sparse Reconstruction

Sparco is a framework for testing and benchmarking algorithms for sparse reconstruction. It includes a large collection of sparse reconstruction problems drawn from the imaging, compressed sensing, and geophysics literature. Sparco is also a framework for implementing new test problems and can be used as a tool for reproducible research. Sparco is implemented entirely in Matlab, and is released as open-source software under the GNU Public License.

[1]  Mauricio D. Sacchi,et al.  Interpolation and extrapolation using a high-resolution discrete Fourier transform , 1998, IEEE Trans. Signal Process..

[2]  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.

[3]  I. Johnstone,et al.  Ideal spatial adaptation by wavelet shrinkage , 1994 .

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

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

[6]  Todd Munson,et al.  Benchmarking optimization software with COPS. , 2001 .

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

[8]  Felix J. Herrmann,et al.  Application of Stable Signal Recovery to Seismic Data Interpolation , 2006 .

[9]  Felix J. Herrmann,et al.  Random sampling: New insights into the reconstruction of coarsely sampled wavefields , 2007 .

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

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

[12]  Mário A. T. Figueiredo,et al.  Gradient Projection for Sparse Reconstruction: Application to Compressed Sensing and Other Inverse Problems , 2007, IEEE Journal of Selected Topics in Signal Processing.

[13]  David L. Donoho,et al.  Sparse Solution Of Underdetermined Linear Equations By Stagewise Orthogonal Matching Pursuit , 2006 .

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

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

[16]  F. Herrmann,et al.  Sparseness-constrained data continuation with frames: Applications to missing traces and aliased signals in 2/3-D , 2005 .

[17]  Nicholas I. M. Gould,et al.  CUTEr and SifDec: A constrained and unconstrained testing environment, revisited , 2003, TOMS.

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

[19]  E. Berg,et al.  In Pursuit of a Root , 2007 .

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

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

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

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

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

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

[26]  Felix J. Herrmann,et al.  Non-parametric seismic data recovery with curvelet frames , 2008 .

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

[28]  F. Herrmann,et al.  Simply denoise: Wavefield reconstruction via jittered undersampling , 2008 .

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

[30]  Frédéric Lesage,et al.  The Application of Compressed Sensing for , 2009 .

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

[32]  Felix J. Herrmann,et al.  Irregular sampling: from aliasing to noise , 2007 .

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

[34]  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.

[35]  Hengyong Yu,et al.  A differentiable Shepp–Logan phantom and its applications in exact cone-beam CT , 2005, Physics in medicine and biology.

[36]  Richard F. Barrett,et al.  Matrix Market: a web resource for test matrix collections , 1996, Quality of Numerical Software.

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

[38]  M. Lustig,et al.  Compressed Sensing MRI , 2008, IEEE Signal Processing Magazine.

[39]  P. Toft.  The Radon Transform - Theory and Implementation , 1996 .

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

[41]  Dmitry M. Malioutov,et al.  A sparse signal reconstruction perspective for source localization with sensor arrays , 2005, IEEE Transactions on Signal Processing.

[42]  D. Donoho,et al.  Sparse nonnegative solution of underdetermined linear equations by linear programming. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

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

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