Separating a Real-Life Nonlinear Image Mixture

When acquiring an image of a paper document, the image printed on the back page sometimes shows through. The mixture of the front- and back-page images thus obtained is markedly nonlinear, and thus constitutes a good real-life test case for nonlinear blind source separation. This paper addresses a difficult version of this problem, corresponding to the use of "onion skin" paper, which results in a relatively strong nonlinearity of the mixture, which becomes close to singular in the lighter regions of the images. The separation is achieved through the MISEP technique, which is an extension of the well known INFOMAX method. The separation results are assessed with objective quality measures. They show an improvement over the results obtained with linear separation, but have room for further improvement

WAVELET BASED NONLINEAR SEPARATION OF IMAGES

This work addresses a real-life problem corresponding to the separation of the nonlinear mixture of images which arises when we scan a paper document and the image from the back page shows through. The proposed solution consists of a non-iterative procedure that is based on two simple observations: (1) the high frequency content of images is sparse, and (2) the image printed on each side of the paper appears more strongly in the mixture acquired from that side than in the mixture acquired from the opposite side. These ideas had already been used in the context of nonlinear denoising source separation (DSS). However, in that method the degree of separation achieved by applying these ideas was relatively weak, and the separation had to be improved by iterating within the DSS scheme. In this paper the application of these ideas is improved by changing the competition function and the wavelet transform that is used. These improvements allow us to achieve a good separation in one shot, without the need to integrate the process into an iterative DSS scheme. The resulting separation process is both nonlinear and non-local. We present experimental results that show that the method achieves a good separation quality

An Extension of Slow Feature Analysis for Nonlinear Blind Source Separation

We present and test an extension of slow feature analysis as a novel approach to nonlinear blind source separation. The algorithm relies on temporal correlations and iteratively reconstructs a set of statistically independent sources from arbitrary nonlinear instantaneous mixtures. Simulations show that it is able to invert a complicated nonlinear mixture of two audio signals with a reliability of more than $90$\%. The algorithm is based on a mathematical analysis of slow feature analysis for the case of input data that are generated from statistically independent sources

IMAGE SEPARATION BASED ON NONSUBSAMPLED CONTOURLET(NSCT)

ABSTRACT When an image or a document on a paper acquired through scannin

Méthodes de séparation aveugle de sources non linéaires, étude du modèle quadratique 2X2

Cette thèse présente des méthodes de séparation aveugle de sources pour un modèle de mélange non-linéaire particulier, le cas quadratique avec auto-termes et termes croisés. Dans la première partie, nous présentons la structure de séparation étudiée qui se décline sous deux formes : étendue ou basique. Les propriétés de ce réseau récurrent sont ensuite analysées (points d'équilibre, stabilité locale). Nous proposons alors deux méthodes de séparation aveugle de sources. La première exploite les cumulants des observations en un bloc placé en amont de la structure récurrente. La deuxième méthode est basée sur une approche par maximum de vraisemblance. Le tout est validé par des simulations numériques.This thesis presents blind source separation (BSS) methods for a particular model of mixture, the quadratic one. The first part presents the separating structure (basic and extended versions).The equilibrium points of the structure and their local stability are then studied. We propose two methods of BSS. The first method uses the cumulants and the second is based on a maximum likelihood approach. We validate our results by numerical tests

Advanced source separation methods with applications to spatio-temporal datasets

Latent variable models are useful tools for statistical data analysis in many applications. Examples of popular models include factor analysis, state-space models and independent component analysis. These types of models can be used for solving the source separation problem in which the latent variables should have a meaningful interpretation and represent the actual sources generating data. Source separation methods is the main focus of this work. Bayesian statistical theory provides a principled way to learn latent variable models and therefore to solve the source separation problem. The first part of this work studies variational Bayesian methods and their application to different latent variable models. The properties of variational Bayesian methods are investigated both theoretically and experimentally using linear source separation models. A new nonlinear factor analysis model which restricts the generative mapping to the practically important case of post-nonlinear mixtures is presented. The variational Bayesian approach to learning nonlinear state-space models is studied as well. This method is applied to the practical problem of detecting changes in the dynamics of complex nonlinear processes. The main drawback of Bayesian methods is their high computational burden. This complicates their use for exploratory data analysis in which observed data regularities often suggest what kind of models could be tried. Therefore, the second part of this work proposes several faster source separation algorithms implemented in a common algorithmic framework. The proposed approaches separate the sources by analyzing their spectral contents, decoupling their dynamic models or by optimizing their prominent variance structures. These algorithms are applied to spatio-temporal datasets containing global climate measurements from a long period of time.reviewe