Reed Muller sensing matrices and the LASSO (Invited paper)

Journal Article

We construct two families of deterministic sensing matrices where the columns are obtained by exponentiating codewords in the quaternary Delsarte-Goethals code DG(m,r). This method of construction results in sensing matrices with low coherence and spectral norm. The first family, which we call Delsarte-Goethals frames, are 2m - dimensional tight frames with redundancy 2rm . The second family, which we call Delsarte-Goethals sieves, are obtained by subsampling the column vectors in a Delsarte-Goethals frame. Different rows of a Delsarte-Goethals sieve may not be orthogonal, and we present an effective algorithm for identifying all pairs of non-orthogonal rows. The pairs turn out to be duplicate measurements and eliminating them leads to a tight frame. Experimental results suggest that all DG(m,r) sieves with m ≤ 15 and r ≥ 2 are tight-frames; there are no duplicate rows. For both families of sensing matrices, we measure accuracy of reconstruction (statistical 0 - 1 loss) and complexity (average reconstruction time) as a function of the sparsity level k. Our results show that DG frames and sieves outperform random Gaussian matrices in terms of noiseless and noisy signal recovery using the LASSO. © 2010 Springer-Verlag.

Full Text

Duke Authors

Cited Authors

  • Calderbank, R; Jafarpour, S

Published Date

  • November 19, 2010

Published In

Volume / Issue

  • 6338 LNCS /

Start / End Page

  • 442 - 463

Electronic International Standard Serial Number (EISSN)

  • 1611-3349

International Standard Serial Number (ISSN)

  • 0302-9743

Digital Object Identifier (DOI)

  • 10.1007/978-3-642-15874-2_37

Citation Source

  • Scopus