Empirical evaluation of a sub-linear time sparse DFT algorithm

Communications in Mathematical Sciences

Volumn 5, Issue 4, 2007, Pages 981-998

  Iwen, Mark A ^a   Gilbert, Anna ^a   Strauss, Martin ^a  

^a UNIVERSITY OF MICHIGAN   (United States)

Author keywords

Compressive sensing; Fourier transforms; Sub linear time algorithms

Indexed keywords

EID: 39149123830     PISSN: 15396746     EISSN: None     Source Type: Journal    
DOI: 10.4310/cms.2007.v5.n4.a13     Document Type: Article

References (20)

1. http://www-personal.umich.edu/~markiwen/.
2. C. Anderson and M.D. Dahleh, Rapid computation of the discrete Fourier transform, SIAM J. Sci. Comput., 17, 913-919, 1996.
3. G. Box and M. Muller, A note on the generation of random normal deviates, Ann. Math. Stat., 29, 610-611, 1958.
4. E. Candes, J. Romberg and T. Tao, Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information, IEEE Trans. Inform. Theory, 52(2), 489-509, 2006.
5. J. Cooley and J. Tukey, An algorithm for the machine calculation of complex Fourier series, Math. Comput., 19, 297-301, 1965.
6. I. Daubechies, O. Runborg and J. Zou, A Sparse spectral method for homogenization multiscale problems, Multiscale Model. Sim., 2007.
7. A. Dutt and V. Rokhlin, Fast Fourier transforms for nonequispaced data, SIAM J. Sci. Comput., 14, 1368-1383, 1993.
8. J. A. Fessler and B.P. Sutton, Nonuniform fast Fourier transforms using min-max interpolation, IEEE Trans. Signal Proc., 51, 560-574, 2003.
9. M. Frigo and S. Johnson, The design and implementation of FFTW3, Proceedings of IEEE, 93(2), 216-231, 2005.
10. A. Gilbert, S. Guha, P. Indyk, S. Muthukrishnan and M. Strauss, Near-optimal sparse Fourier estimation via sampling, ACM STOC, 152-161, 2002.
11. A. Gilbert, S. Muthukrishnan and M. Strauss, Improved Time Bounds for Near-Optimal Sparse Fourier Representations, SPIE, 2005.
12. M. Iwen, unpublished results. http://www-personal.umich.edu/~markiwen/ respub.htm
13. S. Kirolos, J. Laska, M. Wakin, M. Duarte, D. Baron, T. Ragheb, Y. Massoud and R. Baraniuk, Analog-to-information conversion via random demodulation, Proc. IEEE Dallas Circuits and Systems Conference, 2006.
14. J. Laska, S. Kirolos, Y. Massoud, R. Baraniuk, A. Gilbert, M. Iwen and M. Strauss, Random sampling for analog-to-information conversion of wideband signals, Proc. IEEE Dallas Circuits and Systems Conference, 2006.
15. J.Y. Lee and L. Greengard, The type 3 nonuniform FFT and its applications, J. Comput. Phys., 206(1), 1-5, 2005.
16. M. Lustig, D. Donoho and J. Pauly, Sparse MRI. The application of compressed sensing for rapid MR imaging, submitted, 2007.
17. R. Maleh, A.C. Gilbert and M.J. Strauss, Sparse gradient image reconstruction done faster, IEEE International Conference on Image Processing, 2007.
18. M. Rudelson and R. Vershynin, Sparse reconstruction by convex relaxation: Fourier and Gaussian measurements, Conference on Information Sciences and Systems, 2006.
19. J. Tropp and A. Gilbert, Signal recovery from partial information via orthogonal matching pursuit, submitted, 2005.
20. J. Zou, A. Gilbert, M. Strauss and I. Daubechies, Theoretical and experimental analysis of a randomized algorithm for sparse Fourier transform analysis, J. Comput. Phys., 211(2), 572-595, 2006.