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Sparse-based estimation performance for partially known overcomplete large-systems

Abstract : We assume the direct sum A ⊕ B for the signal subspace. As a result of post-measurement, a number of operational contexts presuppose the a priori knowledge of the L B-dimensional "interfering" subspace B and the goal is to estimate the L A amplitudes corresponding to subspace A. Taking into account the knowledge of the orthogonal "interfering" subspace B ⊥, the Bayesian estimation lower bound is derived for the L A-sparse vector in the doubly asymptotic scenario, i.e. N, L A , L B → ∞ with a finite asymptotic ratio. By jointly exploiting the Compressed Sensing (CS) and the Random Matrix Theory (RMT) frameworks, closed-form expressions for the lower bound on the estimation of the non-zero entries of a sparse vector of interest are derived and studied. The derived closed-form expressions enjoy several interesting features: (i) a simple interpretable expression, (ii) a very low computational cost especially in the doubly asymptotic scenario, (iii) an accurate prediction of the mean-square-error (MSE) of popular sparse-based estimators and (iv) the lower bound remains true for any amplitudes vector priors. Finally, several idealized scenarios are compared to the derived bound for a common output signal-to-noise-ratio (SNR) which shows the interest of the joint estimation/rejection methodology derived herein.
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Submitted on : Tuesday, April 25, 2017 - 5:25:08 PM
Last modification on : Saturday, September 24, 2022 - 2:28:05 PM
Long-term archiving on: : Wednesday, July 26, 2017 - 2:35:15 PM

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Guillaume Bouleux, Remy Boyer. Sparse-based estimation performance for partially known overcomplete large-systems. Signal Processing, Elsevier, 2017, 139, pp.70-74. ⟨10.1016/j.sigpro.2017.04.010⟩. ⟨hal-01514154⟩

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