Signal sparsity estimation from compressive noisy projections via γ-sparsified random matrices
C. Ravazzi, S. M. Fosson, T. Bianchi and E. Magli
2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Shanghai, 2016, pp. 4029-4033.
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.