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Reconstruction of signals drawn from a gaussian mixture via noisy compressive measurements

Publication ,  Journal Article
Renna, F; Calderbank, R; Carin, L; Rodrigues, MRD
Published in: IEEE Transactions on Signal Processing
May 1, 2014

This paper determines to within a single measurement the minimum number of measurements required to successfully reconstruct a signal drawn from a Gaussian mixture model in the low-noise regime. The method is to develop upper and lower bounds that are a function of the maximum dimension of the linear subspaces spanned by the Gaussian mixture components. The method not only reveals the existence or absence of a minimum mean-squared error (MMSE) error floor (phase transition) but also provides insight into the MMSE decay via multivariate generalizations of the MMSE dimension and the MMSE power offset, which are a function of the interaction between the geometrical properties of the kernel and the Gaussian mixture. These results apply not only to standard linear random Gaussian measurements but also to linear kernels that minimize the MMSE. It is shown that optimal kernels do not change the number of measurements associated with the MMSE phase transition, rather they affect the sensed power required to achieve a target MMSE in the low-noise regime. Overall, our bounds are tighter and sharper than standard bounds on the minimum number of measurements needed to recover sparse signals associated with a union of subspaces model, as they are not asymptotic in the signal dimension or signal sparsity. © 2014 IEEE.

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Published In

IEEE Transactions on Signal Processing

DOI

ISSN

1053-587X

Publication Date

May 1, 2014

Volume

62

Issue

9

Start / End Page

2265 / 2277

Related Subject Headings

  • Networking & Telecommunications
 

Citation

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Renna, F., Calderbank, R., Carin, L., & Rodrigues, M. R. D. (2014). Reconstruction of signals drawn from a gaussian mixture via noisy compressive measurements. IEEE Transactions on Signal Processing, 62(9), 2265–2277. https://doi.org/10.1109/TSP.2014.2309560
Renna, F., R. Calderbank, L. Carin, and M. R. D. Rodrigues. “Reconstruction of signals drawn from a gaussian mixture via noisy compressive measurements.” IEEE Transactions on Signal Processing 62, no. 9 (May 1, 2014): 2265–77. https://doi.org/10.1109/TSP.2014.2309560.
Renna F, Calderbank R, Carin L, Rodrigues MRD. Reconstruction of signals drawn from a gaussian mixture via noisy compressive measurements. IEEE Transactions on Signal Processing. 2014 May 1;62(9):2265–77.
Renna, F., et al. “Reconstruction of signals drawn from a gaussian mixture via noisy compressive measurements.” IEEE Transactions on Signal Processing, vol. 62, no. 9, May 2014, pp. 2265–77. Scopus, doi:10.1109/TSP.2014.2309560.
Renna F, Calderbank R, Carin L, Rodrigues MRD. Reconstruction of signals drawn from a gaussian mixture via noisy compressive measurements. IEEE Transactions on Signal Processing. 2014 May 1;62(9):2265–2277.

Published In

IEEE Transactions on Signal Processing

DOI

ISSN

1053-587X

Publication Date

May 1, 2014

Volume

62

Issue

9

Start / End Page

2265 / 2277

Related Subject Headings

  • Networking & Telecommunications