Sparsity estimation from compressive projections via sparse random matrices
| Autor: | Enrico Magli, Tiziano Bianchi, Sophie M. Fosson, Chiara Ravazzi |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Sparsity recovery
Compressed sensing High-dimensional statistical inference Gaussian mixture models Maximum likelihood Sparse random matrices Computer science Gaussian lcsh:TK7800-8360 02 engineering and technology 01 natural sciences Signal lcsh:Telecommunication symbols.namesake lcsh:TK5101-6720 0202 electrical engineering electronic engineering information engineering Limit (mathematics) 0101 mathematics Scaling Noise (signal processing) Research 010102 general mathematics lcsh:Electronics 020206 networking & telecommunications Mixture model symbols Random matrix Algorithm |
| Zdroj: | Eurasip Journal on Advances in Signal Processing EURASIP Journal on Advances in Signal Processing 2018 (2018): 1–18. doi:10.1186/s13634-018-0578-0 info:cnr-pdr/source/autori:Ravazzi C.; Fosson S.; Bianchi T.; Magli E./titolo:Sparsity estimation from compressive projections via sparse random matrices/doi:10.1186%2Fs13634-018-0578-0/rivista:EURASIP Journal on Advances in Signal Processing (Print)/anno:2018/pagina_da:1/pagina_a:18/intervallo_pagine:1–18/volume:2018 EURASIP Journal on Advances in Signal Processing, Vol 2018, Iss 1, Pp 1-18 (2018) |
| ISSN: | 1687-6172 |
| DOI: | 10.1186/s13634-018-0578-0 |
| Popis: | The aim of this paper is to develop strategies to estimate the sparsity degree of a signal from compressive projections, without the burden of recovery. We consider both the noise-free and the noisy settings, and we show how to extend the proposed framework to the case of non-exactly sparse signals. The proposed method employs γ-sparsified random matrices and is based on a maximum likelihood (ML) approach, exploiting the property that the acquired measurements are distributed according to a mixture model whose parameters depend on the signal sparsity. In the presence of noise, given the complexity of ML estimation, the probability model is approximated with a two-component Gaussian mixture (2-GMM), which can be easily learned via expectation-maximization. Besides the design of the method, this paper makes two novel contributions. First, in the absence of noise, sufficient conditions on the number of measurements are provided for almost sure exact estimation in different regimes of behavior, defined by the scaling of the measurements sparsity γ and the signal sparsity. In the presence of noise, our second contribution is to prove that the 2-GMM approximation is accurate in the large system limit for a proper choice of γ parameter. Simulations validate our predictions and show that the proposed algorithms outperform the state-of-the-art methods for sparsity estimation. Finally, the estimation strategy is applied to non-exactly sparse signals. The results are very encouraging, suggesting further extension to more general frameworks. |
| Databáze: | OpenAIRE |
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