Consiglio Nazionale delle Ricerche

Tipo di prodottoArticolo in rivista
TitoloSparsity estimation from compressive projections via sparse random matrices
Anno di pubblicazione2018
Autore/iRavazzi C.; Fosson S.; Bianchi T.; Magli E.
Affiliazioni autoriConsiglio Nazionale dell Ricerche, Politecnico di Torino
Autori CNR e affiliazioni
  • inglese
AbstractThe 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 ?-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 ? 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 ? 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.
Lingua abstractinglese
Altro abstract-
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Pagine da1
Pagine a18
Pagine totali18
RivistaEURASIP Journal on Advances in Signal Processing (Print)
Attiva dal 2007
Editore: Hindawi Publishing Corporation - Cairo
Paese di pubblicazione: Egitto
Lingua: inglese
ISSN: 1687-6172
Titolo chiave: EURASIP Journal on Advances in Signal Processing (Print)
Titolo proprio: EURASIP Journal on Advances in Signal Processing (Print)
Titolo abbreviato: EURASIP J. Adv. Signal Process. (Print)
Numero volume della rivista2018
Fascicolo della rivista-
Verificato da refereeSì: Internazionale
Stato della pubblicazionePublished version
Indicizzazione (in banche dati controllate)
  • Scopus (Codice:2-s2.0-85053210093)
Parole chiaveMaximum likelihood, Sparse random matrices, Compressed sensing
Link (URL, URI)
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Data di accettazione-
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Strutture CNR
  • IEIIT — Istituto di elettronica e di ingegneria dell'informazione e delle telecomunicazioni
Moduli CNR
    Progetti Europei-
    • JASP2018_b