Performance of the Delsarte-Goethals frame on clustered sparse vectors

Journal Article (Journal Article)

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.

Full Text

Duke Authors

Cited Authors

  • Duarte, MF; Jafarpour, S; Calderbank, AR

Published Date

  • April 5, 2013

Published In

Volume / Issue

  • 61 / 8

Start / End Page

  • 1998 - 2008

International Standard Serial Number (ISSN)

  • 1053-587X

Digital Object Identifier (DOI)

  • 10.1109/TSP.2013.2242064

Citation Source

  • Scopus