Algorithm 890: Sparco: A testing framework for sparse reconstruction

ACM Transactions on Mathematical Software

Volumn 35, Issue 4, 2009, Pages

  Van Den Berg, Ewout ^a   Friedlander, Michael P ^a   Hennenfent, Gilles ^a   Herrmann, Felix J ^a   Saab, Rayan ^a   Yilmaz, Özgür ^a  

^a UNIVERSITY OF BRITISH COLUMBIA   (Canada)

Author keywords

Compressed sensing; Linear operators; Sparse recovery

Indexed keywords

BENCHMARKING ALGORITHMS; COMPRESSED SENSING; GNU PUBLIC LICENSE; LINEAR OPERATORS; OPEN-SOURCE SOFTWARES; REPRODUCIBLE RESEARCHES; SPARSE RECONSTRUCTION; SPARSE RECOVERY; TEST PROBLEMS; TESTING FRAMEWORKS;

MATLAB; RESTORATION; SIGNAL RECONSTRUCTION;

MATHEMATICAL OPERATORS;

EID: 61349195870     PISSN: 00983500     EISSN: 15577295     Source Type: Journal    
DOI: 10.1145/1462173.1462178     Document Type: Article

References (49)

1. BARANIUK, R., CHOI, H., FERNANDES, F., HENDRICKS, B., NEELAMANI, R., RIBEIRO, V., ROMBERG, J., GOPINATH, R., GUO, H.-T., LANG, M., ODEGARD, J. E., AND WEI, D. 1993. Rice wavelet toolbox. http://www.dsp.rice.edu/software/rwt.shtml.
2. VAN DEN BERG, E. AND FRIEDLANDER, M. P. 2008. Probing the Pareto frontier for basis pursuit solutions. SIAM J. Sci. Comp. 31, 2, 840-912.
3. BOISVERT, R., POZO, R., REMINGTON, K., BARRETT, R., AND DONGARRA, J. 1997. Matrix Market: A Web resource for test matrix collections. In The Quality of Numerical Software: Assessment and Enhancement, R. F. Boisvert, Ed. Chapman & Hall, London, 125-137.
4. CANDÈS, E. J. 2006. Compressive sampling. In Proceedings of the International Congress of Mathematicians.
5. CANDÈS, E. J., DEMANET, L., DONOHO, D. L., AND YING, L.-X. 2007. Curve Lab. http://www.curvelet.org/.
6. 1-magic. http://www.11-magic.org/.
7. CANDÈS, E. J., ROMBERG, J., AND TAO, T. 2006a. Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information. IEEE Trans. Inf. Theory 52, 2, 489-509.
8. CANDÈS, E. J., ROMBERG, J., AND TAO, T. 2006b. Stable signal recovery from incomplete and inaccurate measurements. Commun. Pure Appl. Math. 59, 8, 1207-1223.
9. CANDÈS, E. J. AND TAO, T. 2005. Decoding by linear programming. IEEE Trans. Inf. Theory 51, 12, 4203-4215.
10. CANDÈS, E. J. AND TAO, T. 2006, Near-Optimal signal recovery from random projections: Universal encoding strategies? IEEE Trans. Inf. Theory 52, 12, 5406-5425.
11. CHEN, S. S., DONOHO, D. L., AND SAUNDERS, M. A. 1998. Atomic decomposition by basis pursuit. SIAM J. Sci. Comput. 20, 1, 33-61.
12. COMBETTES, P. L. AND WAJS, V. R. 2005. Signal recovery by proximal forward-backward splitting. Multiscale Modeling and Simul. 4, 4, 1168-1200.
13. DAUBECHIES, I. 1992. Ten Lectures on Wavelets. SIAM, Philadelphia, PA.
14. DAUBECHIES, I., DEFRISE, M., AND DE MOL, C. 2004. An iterative thresholding algorithm for linear inverse problems with a sparsity constraint. Commun. Pure Appl. Math. 57, 1413-1457.
15. DOLAN, E. D. AND MORÉ, J. J. 2000. Benchmarking optimization software with COPS. Tech. rep. ANL/MCS-246, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, IL. Revised January 2001.
16. DONOHO, D. L. 2006a. Compressed sensing. IEEE Trans. Inf. Theory 52, 4, 1289-1306.
17. 1-norm solution is also the sparsest solution. Commun. Pure Appl. Math. 59, 6, 797-829.
18. 1 minimization. Proc. Natl. Acad. Sci. USA 100, 5, 2197-2202.
19. DONOHO, D. L. AND HUO, X. 2001. Uncertainty principles and ideal atomic decomposition. IEEE Trans. Inf. Theory 47, 7, 2845-2862.
20. DONOHO, D. L. AND JOHNSTONE, I. M. 1994. Ideal spatial adaptation by wavelet shrinkage. Biometrika 81, 3, 425-455.
21. DONOHO, D. L., STODDEN, V. C., AND TSAIG, Y. 2007. Sparselab. http://sparselab.stanford.edu/.
22. DONOHO, D. L. AND TANNER, J. 2005. Sparse nonnegative solution of underdetermined linear equations by linear programming. Proc. Natl. Acad. Sci. USA 102, 27, 9446-9451.
23. DONOHO, D. L., TSAIG, Y., DRORI, I., AND STARCK, J.-L. 2006. Sparse solution of underdetermined linear equations by stagewise orthogonal matching pursuit. Tech. rep. 2006-2, Department of Statistics, Stanford University. April.
24. EFRON, B., HASTIE, T, JOHNSTONE, I., AND TIBSHIRANI, R. 2004. Least angle regression. Ann. Statist. 32, 2, 407-499.
25. FIGUEIREDO, M., NOWAK, R., AND WRIGHT, S. J. 2007. Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems. IEEE J. Selected Topics in Signal Process. 1, 4, 586-597.
26. GOULD, N. I. M., ORBAN, D., AND TOINT, PH. L. 2003. CUTEr and SifDec: A constrained and unconstrained testing environment, revisited. ACM Trans. Math. Softw. 29, 4, 373-394.
27. GRIBONVAL, R. AND NIELSEN, M. 2003. Sparse representations in unions of bases. IEEE Trans. Inf. Theory 49, 12, 3320-3325.
28. HALE, E., YIN, W., AND ZHANG, Y 2007. A fixed-point continuation method for 11-regularized minimization with applications to compressed sensing. Tech. rep. TR07-07, Department of Computational and Applied Mathematics, Rice University, Houston, TX.
29. HENNENFENT, G. AND HERRMANN, F. J. 2005. Sparseness-Constrained data continuation with frames: Applications to missing traces and aliased signals in 2/3-D. In SEG International Exposition and 75th Annual Meeting.
30. HENNENFENT, G. AND HERRMANN, F. J. 2006. Application of stable signal recovery to seismic interpolation. In SEG International Exposition and 76th Annual Meeting.
31. HENNENFENT, G. AND HERRMANN, F. J. 2007. Random sampling: New insights into the reconstruction of coarsely-sampled wavefields. In SEG International Exposition and 77th Annual Meeting.
32. HENNENFENT, G. AND HERRMANN, F. J. 2008. Simply denoise: Wavefield reconstruction via jittered undersampling. GEOPHYS. 73, 3, V19-V28.
33. HERRMANN, F. J. AND HENNENFENT, G. 2008. Non-Parametric seismic data recovery with curvelet frames. Geophys. J. Int. 173, 233-248.
34. 1 -regularized least squares. IEEE J. Selected Topics Signal Process. 1, 4, 606-617.
35. LUSTIG, M., DONOHO, D. L., AND PAULY, J. M. 2007a. Sparse MRI Matlab code. http://www.stanford.edu/~mlustig/ SparseMRI.html.
36. LUSTIG, M., DONOHO, D. L., AND PAULY, J. M. 2007b. Sparse MRI: The application of compressed sensing for rapid MR imaging. Magnetic Resonance Med. 58, 6, 1182-1195.
37. LUSTIG, M., DONOHO, D. L., SANTOS, J. M., AND PAULY, J. M. 2007c. Compressed sensing MRI. IEEE Signal Process. Mag. 25, 2, 72-82.
38. MALIOUTOV, D., ÇETIN, M., AND WILLSKY, A. S. 2005. A sparse signal reconstruction perspective for source localization with sensor arrays. IEEE Trans. Signal. Process. 53, 8, 3010-3022.
39. MENDELSON, S., PAJOR, A., AND TOMCZAK-JAEGERMANN, N. 2008. Uniform uncertainty principle for Bernoulli and subGaussian ensembles. Constructive Approximation. To appear.
40. NATARAJAN, B. K. 1995. Sparse approximate solutions to linear systems. SIAM J. Comput. 24, 2, 227-234.
41. OSBORNE, M. R., PRESNELL, B., AND TURLACH, B. A. 2000a. The Lasso and its dual. J. Comput. Graph. Statist. 9, 319-337.
42. OSBORNE, M. R., PRESNELL, B., AND TURLACH, B. A. 2000b. A new approach to variable selection in least squares problems. IMA J. Numer. Anal. 20, 3, 389-403.
43. PATI, Y. C., REZAIIFAR, R., AND KRISHNAPEASAD, P. S. 1993. Orthogonal matching pursuit: Recursive function approximation with applications to wavelet decomposition. In Proceedings of the 27th Annual Asilomar Conference on Signals, Systems and Computers, vol. 1, 40-44.
44. RUDIN, L., OSHER, S., AND FATEMI, E. 1992. Nonlinear total variation based noise removal algorithms. Physica D 60, 259-268.
45. SACCHI, M. D., ULRYCH, T. J., AND WALKER, C. J. 1998. Interpolation and extrapolation using a high-resolution discrete Fourier transform. IEEE Trans. Signal Process. 46, 1, 31-38.
46. TAKHAR, D., LASKA, J. N., WAKIN, M., DUARTE, M., BARON, D., SAEVOTHAM, S., KELLY, K. K., AND BARANIUK, R. G. 2006. A new camera architecture based on optical-domain compression. In Proceedings of the IS&T/SPIE Symposium on Electronic Imaging: Computational Imaging, vol. 6065.
47. TROPP, J. A. 2004. Greed is good: Algorithmic results for sparse approximation. IEEE Trans. Inf. Theory 50, 10, 2231-2242.
48. TROPP, J. A. 2006. Just relax: Convex programming methods for identifying sparse signals in noise. IEEE Trans. Inf. Theory 52, 3, 1030-1051.
49. WANG, D., SAAB, R., YILMAZ, Ö., AND HERRMANN, F. 2008. Bayesian wavefield separation by transform-domain sparsity promotion. Geophys. To appear.