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Performance of the Delsarte-Goethals frame on clustered sparse vectors

Publication ,  Journal Article
Duarte, MF; Jafarpour, S; Calderbank, AR
Published in: IEEE Transactions on Signal Processing
April 5, 2013

The Delsarte-Goethals frame (DGF) has been proposed for deterministic compressive sensing of sparse and compressible signals. Results in compressive sensing theory show that the DGF enables successful recovery of an overwhelming majority of sufficiently sparse signals. However, these results do not give a characterization of the sparse vectors for which the recovery procedure fails. In this paper, we present a formal analysis of the DGF that highlights the presence of clustered sparse vectors within its null space. This in turn implies that sparse recovery performance is diminished for sparse vectors that have their nonzero entries clustered together. Such clustered structure is present in compressive imaging applications, where commonly-used raster scannings of 2-D discrete wavelet transform representations yield clustered sparse representations for natural images. Prior work leverages this structure by proposing specially tailored sparse recovery algorithms that partition the recovery of the input vector into known clustered and unclustered portions. Alternatively, we propose new randomized and deterministic raster scannings for clustered coefficient vectors that improve recovery performance. Experimental results verify the aforementioned analysis and confirm the predicted improvements for both noiseless and noisy measurement regimes. © 1991-2012 IEEE.

Duke Scholars

Published In

IEEE Transactions on Signal Processing

DOI

ISSN

1053-587X

Publication Date

April 5, 2013

Volume

61

Issue

8

Start / End Page

1998 / 2008

Related Subject Headings

  • Networking & Telecommunications
 

Citation

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Duarte, M. F., Jafarpour, S., & Calderbank, A. R. (2013). Performance of the Delsarte-Goethals frame on clustered sparse vectors. IEEE Transactions on Signal Processing, 61(8), 1998–2008. https://doi.org/10.1109/TSP.2013.2242064
Duarte, M. F., S. Jafarpour, and A. R. Calderbank. “Performance of the Delsarte-Goethals frame on clustered sparse vectors.” IEEE Transactions on Signal Processing 61, no. 8 (April 5, 2013): 1998–2008. https://doi.org/10.1109/TSP.2013.2242064.
Duarte MF, Jafarpour S, Calderbank AR. Performance of the Delsarte-Goethals frame on clustered sparse vectors. IEEE Transactions on Signal Processing. 2013 Apr 5;61(8):1998–2008.
Duarte, M. F., et al. “Performance of the Delsarte-Goethals frame on clustered sparse vectors.” IEEE Transactions on Signal Processing, vol. 61, no. 8, Apr. 2013, pp. 1998–2008. Scopus, doi:10.1109/TSP.2013.2242064.
Duarte MF, Jafarpour S, Calderbank AR. Performance of the Delsarte-Goethals frame on clustered sparse vectors. IEEE Transactions on Signal Processing. 2013 Apr 5;61(8):1998–2008.

Published In

IEEE Transactions on Signal Processing

DOI

ISSN

1053-587X

Publication Date

April 5, 2013

Volume

61

Issue

8

Start / End Page

1998 / 2008

Related Subject Headings

  • Networking & Telecommunications