Performance Analysis for Sparse Biased Estimator : Application to Line Spectra Analysis

International audienceDictionary based sparse estimators are based on the matching of continuous parameters of interest to a discretized sampling grid. Generally, the parameters of interest do not lie on this grid and there exists an estimator bias even at high Signal to Noise Ratio (SNR). This is the off-grid problem. In this work, we propose and study analytical expressions of the Bayesian Mean Square Error (BMSE) of dictionary based biased estimators at high SNR. We also show that this class of estimators is efficient and thus reaches the Bayesian Cramér-Rao Bound (BCRB) at high SNR. The proposed results are illustrated in the context of line spectra analysis and several popular sparse estimators are compared to our closed-form expressions of the BMSE

MTF measurements of a type-II superlattice infrared focal plane array sealed in a cryocooler

International audienceIn operational electro-optical systems, infrared focal plane arrays (IR FPA) are integrated in cryocoolers which induce vibrations that may strongly affect their modulation transfer function (MTF). In this paper, we present the MTF measurement of an IR FPA sealed in its cryocooler. The method we use to measure the MTF decorrelates operational constraints and the technological limitations of the IR FPA. The bench is based on the diffraction properties of a continuously self imaging grating (CSIG). The 26 µm pixel size extracted from the MTF measurement is in good agreement with the expected value

Gyromètre a fibre a double conjugaison de phase - étude d'un nouveau matériau photorefractif - réalisation d'un démonstrateur .

Not availabl

GYROMETRE A FIBRE A DOUBLE CONJUGAISON DE PHASE - ETUDE D'UN NOUVEAU MATERIAU PHOTOREFRACTIF - REALISATION D'UN DEMONSTRATEUR

ORSAY-PARIS 11-BU Sciences (914712101) / SudocSudocFranceF

Ba0.77Ca0.23TiO3 (BCT) : a new photorefractive material to replace BaTiO3 in applications

International audienceThe most popular photorefractive material BaTiO3 suffers from a crippling defect when applications are considered: its phase transition around room temperature that can destroy its photorefractive characteristics, if not the crystal itself. Some years ago, University of Osnabrück [1], proposed and successfully grew Ba0.77Ca0.23TiO3 an alloy derived from BaTiO3, in which the phase transition was pushed away towards low temperature. The remaining question was then: does this new material keep the good photorefractive properties that made the success of BaTiO3? We will present here some theoretical and experimental results that allow us to answer this question and that show that despite some differences in the photorefractive properties between BaTiO3 and BCT, the new crystal is an extremely promising materials for photorefractive applications, such as phase conjugation or dynamic holographic intracavity laser mode selection

Comment "robustifier" les estimateurs par dictionnaire face aux erreurs de grille ?

International audienceLet us consider the very general problem of the estimation of a parameter of interest θ ∈ P, where P is a set of continuous values. Sparse based estimation is based on the matching of the parameters of interest to a regular discretization of P, often referred to as the grid. In realistic scenarios, the off-grid error problem is thus inherent to the presence of the grid and limits in a drastic way the estimation performances of the standard sparse estimation algorithms in the high SNR regime where the off-grid error is predominant with respect to the error due to the noise. In this context, numerous contributions in the literature deals with this problem, but according to our knowledge, the proposed approaches can be defined as ad hoc techniques dedicated to a particular estimator. In this work, our objective is to propose a generic post-treatment, called OGEC (Off-Grid Error Correction), in the sense that it can be used to "robustify" against the off-grid problem any existing sparse based estimator. Furthermore, we design this post-treatment to be cheap in term of calculation cost. OGEC being introduced, we derive theoretically its bias and MSE and finally its performances are illustrated in the context of the compressed sampling of non-bandlimited signals.Considérons le problème très général de l'estimation d'un paramètre d'intérêt tel que θ ∈ P où P est un ensemble à valeurs continues. La stratégie des estimateurs à contrainte de parcimonie repose sur la recherche d'un représentant issu d'une discrétisation régulière de l'ensemble P, souvent appelée grille. Dans un contexte réaliste, le problème d'erreur de grille est donc intrinsèque et limite de manière drastique les performances en estimation des algorithmes standards dans le régime des hauts RSBs où l'erreur de grille devient prépondérante au regard de l'erreur due au bruit. Dans ce contexte, il existe dans la littérature de nombreuses contributions traitant de ce problème. Selon nos connaissances du domaine, les approches proposées peuvent être qualifiées de techniques ad-hoc dédiées à un estimateur en particulier. Dans ce travail, notre objectif est de proposer un post-traitement générique, nommé OGEC (Off-Grid Error Correction), dans le sens où celui-ci pourra être exploité pour "robustifier" aux erreurs de grille tout estimateur à contrainte de parcimonie existant dans la littérature. De plus, nous souhaitons que cette sur-couche soit la moins couteuse possible en terme de temps de calcul. Après avoir présenté l'estimateur OGEC, nous analysons son biais et son EQM de manière théorique. Enfin, les performances de l'OGEC sont illustrées dans le contexte de l'échantillonnage comprimé de signaux à bande non-limité

Compressed sensing with uncertainty. The Bayesian estimation perspective

International audienceThe Compressed Sensing (CS) framework outperforms the sampling rate limits given by Shannon’s theory. This gap is possible since it is assumed that the signal of interest admits a linear decomposition of few vectors in a given sparsifying Basis (Fourier, Wavelet, ...). Unfortunately in realistic operating systems, uncertain knowledge of the CS model is inevitable and must be evaluated. Typically, this uncertainty drastically degrades the estimation performance of sparse-based estimators in the low noise variance regime. In this work, the Off-Grid (OG) and Basis Mismatch (BM) problems are compared in a Bayesian estimation perspective. At first glance, we are tempted to think that these two acronyms stand for the same problem. However, by comparing their Bayesian Cramer-Rao Bounds (BCRB) for the estimation of a L-sparse amplitude vector based on N measurements, it is shown that the BM problem has a lower BCRB than the CS one in a general context. To go further into the analysis we provide for i.i.d. Gaussian amplitudes and in the low noise variance regime an interesting closed-form expression of a normalized 2-norm criterion of the difference of the two BCRB matrices. Based on the analysis of this closed-form expression, we obtain two conclusions. Firstly, the two uncertainty problems cannot be confused for a non-zero mismatch error variance and with finite N and L. Secondly, the two problems turn to be similar for any mismatch error variance in the large system regime with constant aspect ratio.

Compressed Sensing with Basis Mismatch : Performance Bounds and Sparse-Based Estimator

International audienceCompressed sensing (CS) is a promising emerging domain which outperforms the classical limit of the Shannon sampling theory if the measurement vector can be approximated as the linear combination of few basis vectors extracted from a redundant dictionary matrix. Unfortunately, in realistic scenario, the knowledge of this basis or equivalently of the entire dictionary is often uncertain, i.e. corrupted by a Basis Mismatch (BM) error. The consequence of the BM problem is that the estimation accuracy in terms of Bayesian Mean Square Error (BMSE) of popular sparse-based estimators collapses even if the support is perfectly estimated and in the high Signal to Noise Ratio (SNR) regime. This saturation effect considerably limits the effective viability of these estimation schemes. In the first part of this work, the Bayesian Cramér-Rao Bound (BCRB) is derived for CS model with unstructured BM. We show that the BCRB foresees the saturation effect of the estimation accuracy of standard sparse-based estimators as for instance the OMP, Cosamp or the BP. In addition, we provide an approximation of this BMSE threshold. In the second part and in the context of the structured BM model, a new estimation scheme called Bias-Correction Estimator (BiCE) is proposed and its statistical properties are studied. The BiCE acts as a post-processing estimation layer for any sparse-based estimator and mitigates considerably the BM degradation. Finally, the BiCE (i) is a blind algorithm, i.e., is unaware of the uncorrupted dictionary matrix, (ii) is generic since it can be associated to any sparse-based estimator, (iii) is fast, i.e., the additional computational cost remains low and (iv) has good statistical properties. To illustrate our results and propositions, the BiCE is applied in the challenging context of the compressive sampling of non-bandlimited impulsive signals