In this paper, we propose a method for estimating the sparsity of a signal from its noisy linear projections without recovering it. The method exploits the property that linear projections acquired using a sparse sensing matrix are distributed according to a mixture distribution whose parameters depend on the signal sparsity. Due to the complexity of the exact mixture model, we introduce an approximate two-component Gaussian mixture model whose parameters can be estimated via expectation-maximization techniques. We demonstrate that the above model is accurate in the large system limit for a proper choice of the sensing matrix sparsifying parameter. Moreover, experimental results demonstrate that the method is robust under different signal-to-noise ratios and outperforms existing sparsity estimation techniques.
Signal sparsity estimation from compressive noisy projections via γ-sparsified random matrices / Ravazzi, Chiara; Fosson, Sophie; Bianchi, Tiziano; Magli, Enrico. - 2016-:(2016), pp. 4029-4033. (Intervento presentato al convegno 41st IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016 tenutosi a Shanghai, China nel 20-25 March 2016) [10.1109/ICASSP.2016.7472434].
Signal sparsity estimation from compressive noisy projections via γ-sparsified random matrices
RAVAZZI, CHIARA;FOSSON, SOPHIE;BIANCHI, TIZIANO;MAGLI, ENRICO
2016
Abstract
In this paper, we propose a method for estimating the sparsity of a signal from its noisy linear projections without recovering it. The method exploits the property that linear projections acquired using a sparse sensing matrix are distributed according to a mixture distribution whose parameters depend on the signal sparsity. Due to the complexity of the exact mixture model, we introduce an approximate two-component Gaussian mixture model whose parameters can be estimated via expectation-maximization techniques. We demonstrate that the above model is accurate in the large system limit for a proper choice of the sensing matrix sparsifying parameter. Moreover, experimental results demonstrate that the method is robust under different signal-to-noise ratios and outperforms existing sparsity estimation techniques.File | Dimensione | Formato | |
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https://hdl.handle.net/11583/2644299
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