Time and spectral domain relative entropy: A new approach to multivariate spectral estimation

The concept of spectral relative entropy rate is introduced for jointly stationary Gaussian processes. Using classical information-theoretic results, we establish a remarkable connection between time and spectral domain relative entropy rates. This naturally leads to a new spectral estimation technique where a multivariate version of the Itakura-Saito distance is employed}. It may be viewed as an extension of the approach, called THREE, introduced by Byrnes, Georgiou and Lindquist in 2000 which, in turn, followed in the footsteps of the Burg-Jaynes Maximum Entropy Method. Spectral estimation is here recast in the form of a constrained spectrum approximation problem where the distance is equal to the processes relative entropy rate. The corresponding solution entails a complexity upper bound which improves on the one so far available in the multichannel framework. Indeed, it is equal to the one featured by THREE in the scalar case. The solution is computed via a globally convergent matricial Newton-type algorithm. Simulations suggest the effectiveness of the new technique in tackling multivariate spectral estimation tasks, especially in the case of short data records.Comment: 32 pages, submitted for publicatio

Sunyaev-Zel'dovich clusters reconstruction in multiband bolometer camera surveys

We present a new method for the reconstruction of Sunyaev-Zel'dovich (SZ) galaxy clusters in future SZ-survey experiments using multiband bolometer cameras such as Olimpo, APEX, or Planck. Our goal is to optimise SZ-Cluster extraction from our observed noisy maps. We wish to emphasize that none of the algorithms used in the detection chain is tuned on prior knowledge on the SZ -Cluster signal, or other astrophysical sources (Optical Spectrum, Noise Covariance Matrix, or covariance of SZ Cluster wavelet coefficients). First, a blind separation of the different astrophysical components which contribute to the observations is conducted using an Independent Component Analysis (ICA) method. Then, a recent non linear filtering technique in the wavelet domain, based on multiscale entropy and the False Discovery Rate (FDR) method, is used to detect and reconstruct the galaxy clusters. Finally, we use the Source Extractor software to identify the detected clusters. The proposed method was applied on realistic simulations of observations. As for global detection efficiency, this new method is impressive as it provides comparable results to Pierpaoli et al. method being however a blind algorithm. Preprint with full resolution figures is available at the URL: w10-dapnia.saclay.cea.fr/Phocea/Vie_des_labos/Ast/ast_visu.php?id_ast=728Comment: Submitted to A&A. 32 Pages, text onl

Sparse component separation for accurate CMB map estimation

The Cosmological Microwave Background (CMB) is of premier importance for the cosmologists to study the birth of our universe. Unfortunately, most CMB experiments such as COBE, WMAP or Planck do not provide a direct measure of the cosmological signal; CMB is mixed up with galactic foregrounds and point sources. For the sake of scientific exploitation, measuring the CMB requires extracting several different astrophysical components (CMB, Sunyaev-Zel'dovich clusters, galactic dust) form multi-wavelength observations. Mathematically speaking, the problem of disentangling the CMB map from the galactic foregrounds amounts to a component or source separation problem. In the field of CMB studies, a very large range of source separation methods have been applied which all differ from each other in the way they model the data and the criteria they rely on to separate components. Two main difficulties are i) the instrument's beam varies across frequencies and ii) the emission laws of most astrophysical components vary across pixels. This paper aims at introducing a very accurate modeling of CMB data, based on sparsity, accounting for beams variability across frequencies as well as spatial variations of the components' spectral characteristics. Based on this new sparse modeling of the data, a sparsity-based component separation method coined Local-Generalized Morphological Component Analysis (L-GMCA) is described. Extensive numerical experiments have been carried out with simulated Planck data. These experiments show the high efficiency of the proposed component separation methods to estimate a clean CMB map with a very low foreground contamination, which makes L-GMCA of prime interest for CMB studies.Comment: submitted to A&

Rational approximations of spectral densities based on the Alpha divergence

We approximate a given rational spectral density by one that is consistent with prescribed second-order statistics. Such an approximation is obtained by minimizing a suitable distance from the given spectrum and under the constraints corresponding to imposing the given second-order statistics. Here, we consider the Alpha divergence family as a distance measure. We show that the corresponding approximation problem leads to a family of rational solutions. Secondly, such a family contains the solution which generalizes the Kullback-Leibler solution proposed by Georgiou and Lindquist in 2003. Finally, numerical simulations suggest that this family contains solutions close to the non-rational solution given by the principle of minimum discrimination information.Comment: to appear in the Mathematics of Control, Signals, and System

Multivariate Spectral Estimation based on the concept of Optimal Prediction

In this technical note, we deal with a spectrum approximation problem arising in THREE-like multivariate spectral estimation approaches. The solution to the problem minimizes a suitable divergence index with respect to an a priori spectral density. We derive a new divergence family between multivariate spectral densities which takes root in the prediction theory. Under mild assumptions on the a priori spectral density, the approximation problem, based on this new divergence family, admits a family of solutions. Moreover, an upper bound on the complexity degree of these solutions is provided

Rank-1 Constrained Multichannel Wiener Filter for Speech Recognition in Noisy Environments

Multichannel linear filters, such as the Multichannel Wiener Filter (MWF) and the Generalized Eigenvalue (GEV) beamformer are popular signal processing techniques which can improve speech recognition performance. In this paper, we present an experimental study on these linear filters in a specific speech recognition task, namely the CHiME-4 challenge, which features real recordings in multiple noisy environments. Specifically, the rank-1 MWF is employed for noise reduction and a new constant residual noise power constraint is derived which enhances the recognition performance. To fulfill the underlying rank-1 assumption, the speech covariance matrix is reconstructed based on eigenvectors or generalized eigenvectors. Then the rank-1 constrained MWF is evaluated with alternative multichannel linear filters under the same framework, which involves a Bidirectional Long Short-Term Memory (BLSTM) network for mask estimation. The proposed filter outperforms alternative ones, leading to a 40% relative Word Error Rate (WER) reduction compared with the baseline Weighted Delay and Sum (WDAS) beamformer on the real test set, and a 15% relative WER reduction compared with the GEV-BAN method. The results also suggest that the speech recognition accuracy correlates more with the Mel-frequency cepstral coefficients (MFCC) feature variance than with the noise reduction or the speech distortion level.Comment: for Computer Speech and Languag

Realization of Heavy Local Fermi Liquid and Non-Fermi Liquid in f2^2 Crystalline-Electric-Field Singlet-Triplet Configuration

Using the numerical renormalization group method, we investigate an extended Anderson model, in which correlated electrons with the $\Gamma_1$(singlet)-$\Gamma4$(triplet) f$^2$ crystalline-electric-field (CEF) configuration hybridize with conduction electrons of $\Gamma_7$(doublet) and $\Gamma_8$ (quartet) under cubic $O_h$ symmetry, from a strong spin-orbit interaction limit. For the case of the parameters relevant to PrFe4P12, the system is under competition between the CEF singlet fixed point and the multichannel Kondo non-Fermi liquid fixed point arising from the quadrupolar coupling between the impurity with pseudospin 1 and the conduction electron with pseudospin 3/2 . We consider that this result reveals the origin of the heaviness of the effective mass and non-Fermi liquid behavior of the Pr- based filled skutterudite compounds.Comment: 9 pages, 5 figure