Rima Guidara

Blind Separation of Nonstationary Markovian Sources Using an Equivariant Newton–Raphson Algorithm

This letter presents a new maximum likelihood method for blindly separating linear instantaneous source mixtures, where source signals are assumed to be mutually independent, Markovian and possibly nonstationary. The proposed approach first extends previous works, by Hosseini to possibly nonstationary sources using two approaches based on blocking and kernel smoothing, respectively. Moreover, to reduce time consumption, we propose an equivariant modified Newton-Raphson algorithm to solve the estimating equations, and we introduce polynomial estimators for the conditional score functions used in our method. Experimental results, both for artificial and real (speech) signals, prove the better performance of our method as compared to various classical blind separation algorithms.

Maximum Likelihood Blind Image Separation Using Nonsymmetrical Half-Plane Markov Random Fields

This paper presents a maximum likelihood approach for blindly separating linear instantaneous mixtures of images. The spatial autocorrelation within each image is described using nonsymmetrical half-plane (NSHP) Markov random fields in order to simplify the joint probability density functions of the source images. A first implementation assuming stationary sources is presented. It is then extended to a more realistic nonstationary image model: two approaches, respectively based on blocking and kernel smoothing, are proposed to cope with the nonstationarity of the images. The estimation of the mixing matrix is performed using an iterative equivariant version of the Newton-Raphson algorithm. Moreover, score functions, required for the computation of the updating rule, are approximated at each iteration by parametric polynomial estimators. Results achieved with artificial mixtures of both artificial and real-world images, including an astrophysical application, clearly prove the high performance of our methods, as compared to classical algorithms.

Markovian blind image separation

We recently proposed a markovian image separation method. The proposed algorithm is however very time consuming so that it cannot be applied to large-size real-world images. In this paper, we propose two major modifications i.e. utilization of a low-cost parametric score function estimator and derivation of a modified equivariant version of Newton-Raphson algorithm for solving the estimating equations. These modifications make the algorithm much faster and allow us to perform more experiments with artificial and real data which are presented in the paper.

A new unsupervised method for hyperspectral image unmixing using a linear-quadratic model

This paper deals with pixel unmixing in hyperspectral remote sensing images. The surface covered by one pixel of these images may contain more than one material component. Thus, the spectrum obtained from such a pixel may result from different contributions of several materials. Using a blind source separation (BSS) method, we aim at decomposing each mixed pixel spectrum into several pure material spectra and their relative contributions. Due to the non-flat landscape, for example in urban areas, the resulting spectrum is obtained from reflections between the various surfaces. As a result, the classical linear mixing model, generally used in BSS methods, is no longer valid. In this work, we propose a new non-linear unmixing method for hyperspectral remote sensing images using a linear-quadratic model. Our approach starts by estimating the number of pure materials called endmembers. Then, supposing the existence of at least two pure pixels per material in the image, it achieves source separation by going through the following stages: endmember spectra estimation, classification into clusters, and estimation of abundance and reflection fractions. Experimental results on artificial mixtures of real spectra confirm the effectiveness of the proposed method.

A map-based NMF approach to hyperspectral image unmixing using a linear-quadratic mixture model

In this paper, we address the problem of spectral unmixing in urban hyperspectral images using a Maximum A Posteriori (MAP)-based Non-negative Matrix Factorization (NMF) approach. Considering a Linear-Quadratic (LQ) mixing model, we seek to decompose the spectrum observed in each pixel of the image into a set of pure material spectra, as well as their abundance fractions and the mixing coefficients associated with products of these pure material spectra. The main idea of the proposed method is to take into account the available prior information about the unknown parameters for a better estimation of them. To this end, we first derive a MAP-based cost function, then minimize it using a projected gradient algorithm by modifying a recently proposed NMF method adapted to LQ mixtures. Simulation results confirm the relevance of our approach.

Blind separation of non-stationary images using Markov models

In recent works, we presented a blind image separation method based on a maximum likelihood approach, where we supposed the sources to be stationary, spatially autocorrelated and following Markov models. To make this method more adapted to real-world images, we here propose to extend it to non-stationary image separation. Two approaches, respectively based on blocking and kernel smoothing, are then used for the estimation of source score functions required for implementing the maximum likelihood approach, in order to allow them to vary within images. The performance of the proposed algorithm, tested on both artificial and real images, is compared to the stationary Markovian approach, and then to some classical blind source separation methods.

A second-order blind source separation method for bilinear mixtures

In this paper, we are interested in the problem of Blind Source Separation using a Second-order Statistics (SOS) method in order to separate autocorrelated and mutually independent sources mixed according to a bilinear (BL) model. In this context, we propose a new approach called Bilinear Second-order Blind Source Separation, which is an extension of linear SOS methods, devoted to separate sources present in BL mixtures. These sources, called extended sources, include the actual sources and their products. We first study the statistical properties of the different extended sources, in order to verify the assumption of identifiability when the actual sources are zero-mean and when they are not. Then, we present the different steps performed in order to estimate these actual centred sources and to extract the actual mixing parameters. The obtained results using artificial mixtures of synthetic and real sources confirm the effectiveness of the new proposed approach.