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

Post-Nonlinear Mixtures and Beyond

Although sources in general nonlinear mixturm arc not separable iising only statistical independence, a special and realistic case of nonlinear mixtnres, the post nonlinear (PNL) mixture is separable choosing a suited separating system. Then, a natural approach is based on the estimation of tho separating Bystem parameters by minimizing an indcpendence criterion, like estimated mwce mutual information. This class of methods requires higher (than 2) order statistics, and cannot separate Gaarsian sources. However, use of [weak) prior, like source temporal correlation or nonstationarity, leads to other source separation Jgw rithms, which are able to separate Gaussian sourra, and can even, for a few of them, works with second-order statistics. Recently, modeling time correlated s011rces by Markov models, we propose vcry efficient algorithms hmed on minimization of the conditional mutual information. Currently, using the prior of temporally correlated sources, we investigate the fesihility of inverting PNL mixtures with non-bijectiw non-liacarities, like quadratic functions. In this paper, we review the main ICA and BSS results for riunlinear mixtures, present PNL models and algorithms, and finish with advanced resutts using temporally correlated snu~s

A Blind Source Separation Method for Chemical Sensor Arrays based on a Second-order mixing model

International audienceIn this paper we propose a blind source separation method to process the data acquired by an array of ion-selective electrodes in order to measure the ionic activity of different ions in an aqueous solution. While this problem has already been studied in the past, the method presented differs from the ones previously analyzed by approximating the mixing function by a second-degree polynomial, and using a method based on the differential of the mutual information to adjust the parameter values. Experimental results, both with synthetic and real data, suggest that the algorithm proposed is more accurate than the other models in the literature

A Fast Gradient Approximation for Nonlinear Blind Signal Processing

When dealing with nonlinear blind processing algorithms (deconvolution or post-nonlinear source separation), complex mathematical estimations must be done giving as a result very slow algorithms. This is the case, for example, in speech processing, spike signals deconvolution or microarray data analysis. In this paper, we propose a simple method to reduce computational time for the inversion of Wiener systems or the separation of post-nonlinear mixtures, by using a linear approximation in a minimum mutual information algorithm. Simulation results demonstrate that linear spline interpolation is fast and accurate, obtaining very good results (similar to those obtained without approximation) while computational time is dramatically decreased. On the other hand, cubic spline interpolation also obtains similar good results, but due to its intrinsic complexity, the global algorithm is much more slow and hence not useful for our purpose

Application of the Mutual Information Minimization to speaker recognition / identification improvement

In this paper we propose the inversion of nonlinear distortions in order to improve the recognition rates of a speaker recognizer system. We study the effect of saturations on the test signals, trying to take into account real situations where the training material has been recorded in a controlled situation but the testing signals present some mismatch with the input signal level (saturations). The experimental results for speaker recognition shows that a combination of several strategies can improve the recognition rates with saturated test sentences from 80% to 89.39%, while the results with clean speech (without saturation) is 87.76% for one microphone, and for speaker identification can reduce the minimum detection cost function with saturated test sentences from 6.42% to 4.15%, while the results with clean speech (without saturation) is 5.74% for one microphone and 7.02% for the other one

Hyperspectral Unmixing Overview: Geometrical, Statistical, and Sparse Regression-Based Approaches

Imaging spectrometers measure electromagnetic energy scattered in their instantaneous field view in hundreds or thousands of spectral channels with higher spectral resolution than multispectral cameras. Imaging spectrometers are therefore often referred to as hyperspectral cameras (HSCs). Higher spectral resolution enables material identification via spectroscopic analysis, which facilitates countless applications that require identifying materials in scenarios unsuitable for classical spectroscopic analysis. Due to low spatial resolution of HSCs, microscopic material mixing, and multiple scattering, spectra measured by HSCs are mixtures of spectra of materials in a scene. Thus, accurate estimation requires unmixing. Pixels are assumed to be mixtures of a few materials, called endmembers. Unmixing involves estimating all or some of: the number of endmembers, their spectral signatures, and their abundances at each pixel. Unmixing is a challenging, ill-posed inverse problem because of model inaccuracies, observation noise, environmental conditions, endmember variability, and data set size. Researchers have devised and investigated many models searching for robust, stable, tractable, and accurate unmixing algorithms. This paper presents an overview of unmixing methods from the time of Keshava and Mustard's unmixing tutorial [1] to the present. Mixing models are first discussed. Signal-subspace, geometrical, statistical, sparsity-based, and spatial-contextual unmixing algorithms are described. Mathematical problems and potential solutions are described. Algorithm characteristics are illustrated experimentally.Comment: This work has been accepted for publication in IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensin

Contributions to theory and algorithms of independent component analysis and signal separation

This thesis addresses the problem of blind signal separation (BSS) using independent component analysis (ICA). In blind signal separation, signals from multiple sources arrive simultaneously at a sensor array, so that each sensor array output contains a mixture of source signals. Sets of sensor outputs are processed to recover the source signals or to identify the mixing system. The term blind refers to the fact that no explicit knowledge of source signals or mixing system is available. Independent component analysis approach uses statistical independence of the source signals to solve the blind signal separation problems. Application domains for the material presented in this thesis include communications, biomedical, audio, image, and sensor array signal processing. In this thesis reliable algorithms for ICA-based blind source separation are developed. In blind source separation problem the goal is to recover all original source signals using the observed mixtures only. The objective is to develop algorithms that are either adaptive to unknown source distributions or do not need to utilize the source distribution information at all. Two parametric methods that can adapt to a wide class of source distributions including skewed distributions are proposed. Another nonparametric technique with desirable large sample properties is also proposed. It is based on characteristic functions and thereby avoids the need to model the source distributions. Experimental results showing reliable performance are given on all of the presented methods. In this thesis theoretical conditions under which instantaneous ICA-based blind signal processing problems can be solved are established. These results extend the celebrated results by Comon of the traditional linear real-valued model. The results are further extended to complex-valued signals and to nonlinear mixing systems. Conditions for identification, uniqueness, and separation are established both for real and complex-valued linear models, and for a proposed class of non-linear mixing systems.reviewe