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Sensitivity to basis mismatch in compressed sensing

Publication ,  Journal Article
Chi, Y; Pezeshki, A; Scharf, L; Calderbank, R
Published in: ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
January 1, 2010

Compressed sensing theory suggests that successful inversion of an image of the physical world from its modal parameters can be achieved at measurement dimensions far lower than the image dimension, provided that the image is sparse in an a priori known basis. The assumed basis for sparsity typically corresponds to a gridding of the parameter space, e.g., an DFT grid in spectrum analysis. However, in reality no physical field is sparse in the DFT basis or in an a priori known basis. No matter how finely we grid the parameter space the sources may not lie in the center of the grid cells and there is always mismatch between the assumed and the actual bases for sparsity. In this paper, we study the sensitivity of compressed sensing (basis pursuit to be exact) to mismatch between the assumed and the actual sparsity bases. Our mathematical analysis and numerical examples show that the performance of basis pursuit degrades considerably in the presence of basis mismatch. ©2010 IEEE.

Duke Scholars

Published In

ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings

DOI

ISSN

1520-6149

Publication Date

January 1, 2010

Start / End Page

3930 / 3933
 

Citation

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Chi, Y., Pezeshki, A., Scharf, L., & Calderbank, R. (2010). Sensitivity to basis mismatch in compressed sensing. ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings, 3930–3933. https://doi.org/10.1109/ICASSP.2010.5495800
Chi, Y., A. Pezeshki, L. Scharf, and R. Calderbank. “Sensitivity to basis mismatch in compressed sensing.” ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings, January 1, 2010, 3930–33. https://doi.org/10.1109/ICASSP.2010.5495800.
Chi Y, Pezeshki A, Scharf L, Calderbank R. Sensitivity to basis mismatch in compressed sensing. ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings. 2010 Jan 1;3930–3.
Chi, Y., et al. “Sensitivity to basis mismatch in compressed sensing.” ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings, Jan. 2010, pp. 3930–33. Scopus, doi:10.1109/ICASSP.2010.5495800.
Chi Y, Pezeshki A, Scharf L, Calderbank R. Sensitivity to basis mismatch in compressed sensing. ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings. 2010 Jan 1;3930–3933.

Published In

ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings

DOI

ISSN

1520-6149

Publication Date

January 1, 2010

Start / End Page

3930 / 3933