Sparse-based estimators improvement in case of basis mismatch

Abstract : Compressed sensing theory promises to sample sparse signals using a limited number of samples. It also resolves the problem of under-determined systems of linear equations when the unknown vector is sparse. Those promising applications induced a growing interest for this field in the past decade. In compressed sensing, the sparse signal estimation is performed using the knowledge of the dictionary used to sample the signal. However, dictionary mismatch often occurs in practical applications, in which case the estimation algorithm uses an uncertain dictionary knowledge. This mismatch introduces an estimation bias even when the noise is low and the support (i.e. location of non-zero amplitudes) is perfectly estimated. In this paper we consider that the dictionary suffers from a structured mismatch, this type of error being of particular interest in sparse estimation applications. We propose the Bias-Correction Estimator (BiCE) post-processing step which enhances the non-zero amplitude estimation of any sparse-based estimator in the presence of a structured dictionary mismatch. We give the theoretical Bayesian Mean Square Error of the proposed estimator and show its statistical efficiency in the low noise variance regime.
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Conference papers
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https://hal-supelec.archives-ouvertes.fr/hal-01245384
Contributor : Sylvie Marcos <>
Submitted on : Thursday, December 17, 2015 - 10:18:57 AM
Last modification on : Wednesday, July 24, 2019 - 8:36:03 PM

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  • HAL Id : hal-01245384, version 1

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Stéphanie Bernhardt, Remy Boyer, Sylvie Marcos, Pascal Larzabal. Sparse-based estimators improvement in case of basis mismatch. IEEE 6th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP 2015) , Dec 2015, Cancùn, Mexico. ⟨hal-01245384⟩

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