Eric Moreau

A robust algorithm for convolutive blind source separation in presence of noise

We consider the blind source separation (BSS) problem in the noisy context. We propose a new methodology in order to enhance separation performances in terms of efficiency and robustness. Our approach consists in denoising the observed signals through the minimization of their total variation, and then minimizing divergence separation criteria combined with the total variation of the estimated source signals. We show by the way that the method leads to some projection problems that are solved by means of projected gradient algorithms. The efficiency and robustness of the proposed algorithm using Hellinger divergence are illustrated and compared with the classical mutual information approach through numerical simulations.

An iterative algorithm for estimation of linear frequency modulated signal parameters

We consider the problem of estimation of a nonstationary signal. The time-frequency characteristics and, more precisely, the instantaneous frequency (IF) of such a signal can be highlighted by the Wigner-Ville transform (WVT). Using the properties of the cross WVT, we develop an iterative algorithm taking into consideration the presence of wrong frequencies in the estimated IF sequence of the signal. Finally, computer simulations are performed in order to illustrate the behavior of this iterative scheme.

Convolutional neural network for video fire and smoke detection

Research on video analysis for fire detection has become a hot topic in computer vision. However, the conventional algorithms use exclusively rule-based models and features vector to classify whether a frame is fire or not. These features are difficult to define and depend largely on the kind of fire observed. The outcome leads to low detection rate and high false-alarm rate. A different approach for this problem is to use a learning algorithm to extract the useful features instead of using an expert to build them. In this paper, we propose a convolutional neural network (CNN) for identifying fire in videos. Convolutional neural network are shown to perform very well in the area of object classification. This network has the ability to perform feature extraction and classification within the same architecture. Tested on real video sequences, the proposed approach achieves better classification performance as some of relevant conventional video fire detection methods and indicates that using CNN to detect fire in videos is very promising.

A Decoupled Jacobi-Like Algorithm for Non-Unitary Joint Diagonalization of Complex-Valued Matrices

We consider the problem of non-orthogonal joint diagonalization of a set of complex matrices. This appears in many signal processing problems and is instrumental in source separation. We propose a new Jacobi-like algorithm based both on a special parameterization of the diagonalizing matrix and on an adapted local criterion. The optimization scheme is based on an alternate estimation of the useful parameters. Numerical simulations illustrate the overall very good performances of the proposed algorithm in comparison to two other Jacobi-like algorithms and to a global algorithm existing in the literature.

A Coordinate Descent Algorithm for Complex Joint Diagonalization Under Hermitian and Transpose Congruences

This paper deals with the problem of joint complex matrix diagonalization by considering both the Hermitian and transpose congruences. We address the general case where the searched diagonalizing matrix is a priori nonunitary. Based on the minimization of a quadratic criterion, we propose a flexible algorithm in the sense that it allows to directly consider a rectangular diagonalizing matrix and to take into consideration both the Hermitian and transpose congruences within the same framework. The proposed algorithm is a coordinate descent algorithm that is based on an approximate criterion leading to the analytical derivation of the minima arguments. Computer simulations are drawn to illustrate the usefulness and performances of the algorithm and a comparison to state-of-the-art algorithms is presented. Finally, an application to independent component analysis based on fourth-order statistics is also presented.

Fast communication: New blind source separation method of independent/dependent sources

We introduce a new blind source separation approach, based on modified Kullback-Leibler divergence between copula densities, for both independent and dependent source component signals. In the classical case of independent source components, the proposed method generalizes the mutual information (between probability densities) procedure. Moreover, it has the great advantage to be naturally extensible to separate mixtures of dependent source components. Simulation results are presented showing the convergence and the efficiency of the proposed algorithms.

Jacobi like algorithm for non-orthogonal joint diagonalization of hermitian matrices

In this paper, we consider the problem of non-orthogonal joint diagonalization of a set of hermitian matrices. This appears in many blind signal processing problems as source separation and independent component analysis. We propose a new Jacobi like algorithm based on a LU decomposition. The main point consists of the analytical derivation of the elementary two by two matrix. In order to determine the diagonalizing matrix parameters, we propose a useful approximation. Numerical simulations illustrate the overall good performances of the proposed algorithm in comparison to two other Jacobi like algorithms existing in the literature.

Fast Jacobi algorithm for non-orthogonal joint diagonalization of non-symmetric third-order tensors

We consider the problem of non-orthogonal joint diagonalization of a set of non-symmetric real-valued third-order tensors. This appears in many signal processing problems and it is instrumental in source separation. We propose a new Jacobi-like algorithm based on an LU decomposition of the so-called diagonalizing matrices. The parameters estimation is done entirely analytically following a strategy based on a classical inverse criterion and a fully decoupled estimation. One important point is that the diagonalization is directly done on the set of third-order tensors and not on their unfolded version. Computer simulations illustrate the overall good performances of the proposed algorithm.

A coupled joint eigenvalue decomposition algorithm for canonical polyadic decomposition of tensors

In this paper we propose a novel algorithm to compute the joint eigenvalue decomposition of a set of squares matrices. This problem is at the heart of recent direct canonical polyadic decomposition algorithms. Contrary to the existing approaches the proposed algorithm can deal equally with real or complex-valued matrices without any modifications. The algorithm is based on the algebraic polar decomposition which allows to make the optimization step directly with complex parameters. Furthermore, both factorization matrices are estimated jointly. This “coupled” approach allows us to limit the numerical complexity of the algorithm. We then show with the help of numerical simulations that this approach is suitable for tensors canonical polyadic decomposition.

On convolutive Blind Source Separation in a noisy context and a total variation regularization

We propose a new strategy for improving classical Blind Source Separation (BSS) methods. This strategy consists in denoising both the observed and the estimated source signals, and is based on the minimization of a regularized criterion which takes into account the Total Variation of the signal. We prove by the way that the method leads to a projection problem which is solved by means of projected gradient algorithm. The effectiveness and the robustness of the proposed separating process are shown on numerical examples.