Flexible methods for blind separation of complex signals

One of the main matter in Blind Source Separation (BSS) performed with a neural network approach is the choice of the nonlinear activation function (AF). In fact if the shape of the activation function is chosen as the cumulative density function (c.d.f.) of the original source the problem is solved. For this scope in this thesis a flexible approach is introduced and the shape of the activation functions is changed during the learning process using the so-called “spline functions”. The problem is complicated in the case of separation of complex sources where there is the problem of the dichotomy between analyticity and boundedness of the complex activation functions. The problem is solved introducing the “splitting function” model as activation function. The “splitting function” is a couple of “spline function” which wind off the real and the imaginary part of the complex activation function, each of one depending from the real and imaginary variable. A more realistic model is the “generalized splitting function”, which is formed by a couple of two bi-dimensional functions (surfaces), one for the real and one for the imaginary part of the complex function, each depending by both the real and imaginary part of the complex variable. Unfortunately the linear environment is unrealistic in many practical applications. In this way there is the need of extending BSS problem in the nonlinear environment: in this case both the activation function than the nonlinear distorting function are realized by the “splitting function” made of “spline function”. The complex and instantaneous separation in linear and nonlinear environment allow us to perform a complex-valued extension of the well-known INFOMAX algorithm in several practical situations, such as convolutive mixtures, fMRI signal analysis and bandpass signal transmission. In addition advanced characteristics on the proposed approach are introduced and deeply described. First of all it is shows as splines are universal nonlinear functions for BSS problem: they are able to perform separation in anyway. Then it is analyzed as the “splitting solution” allows the algorithm to obtain a phase recovery: usually there is a phase ambiguity. Finally a Cramér-Rao lower bound for ICA is discussed. Several experimental results, tested by different objective indexes, show the effectiveness of the proposed approaches

Flexible methods for blind separation of complex signals

One of the main matter in Blind Source Separation (BSS) performed with a neural network approach is the choice of the nonlinear activation function (AF). In fact if the shape of the activation function is chosen as the cumulative density function (c.d.f.) of the original source the problem is solved. For this scope in this thesis a flexible approach is introduced and the shape of the activation functions is changed during the learning process using the so-called “spline functions”. The problem is complicated in the case of separation of complex sources where there is the problem of the dichotomy between analyticity and boundedness of the complex activation functions. The problem is solved introducing the “splitting function” model as activation function. The “splitting function” is a couple of “spline function” which wind off the real and the imaginary part of the complex activation function, each of one depending from the real and imaginary variable. A more realistic model is the “generalized splitting function”, which is formed by a couple of two bi-dimensional functions (surfaces), one for the real and one for the imaginary part of the complex function, each depending by both the real and imaginary part of the complex variable. Unfortunately the linear environment is unrealistic in many practical applications. In this way there is the need of extending BSS problem in the nonlinear environment: in this case both the activation function than the nonlinear distorting function are realized by the “splitting function” made of “spline function”. The complex and instantaneous separation in linear and nonlinear environment allow us to perform a complex-valued extension of the well-known INFOMAX algorithm in several practical situations, such as convolutive mixtures, fMRI signal analysis and bandpass signal transmission. In addition advanced characteristics on the proposed approach are introduced and deeply described. First of all it is shows as splines are universal nonlinear functions for BSS problem: they are able to perform separation in anyway. Then it is analyzed as the “splitting solution” allows the algorithm to obtain a phase recovery: usually there is a phase ambiguity. Finally a Cramér-Rao lower bound for ICA is discussed. Several experimental results, tested by different objective indexes, show the effectiveness of the proposed approaches

ID Photograph hashing : a global approach

This thesis addresses the question of the authenticity of identity photographs, part of the documents required in controlled access. Since sophisticated means of reproduction are publicly available, new methods / techniques should prevent tampering and unauthorized reproduction of the photograph. This thesis proposes a hashing method for the authentication of the identity photographs, robust to print-and-scan. This study focuses also on the effects of digitization at hash level. The developed algorithm performs a dimension reduction, based on independent component analysis (ICA). In the learning stage, the subspace projection is obtained by applying ICA and then reduced according to an original entropic selection strategy. In the extraction stage, the coefficients obtained after projecting the identity image on the subspace are quantified and binarized to obtain the hash value. The study reveals the effects of the scanning noise on the hash values of the identity photographs and shows that the proposed method is robust to the print-and-scan attack. The approach focusing on robust hashing of a restricted class of images (identity) differs from classical approaches that address any imageCette thèse traite de la question de l’authenticité des photographies d’identité, partie intégrante des documents nécessaires lors d’un contrôle d’accès. Alors que les moyens de reproduction sophistiqués sont accessibles au grand public, de nouvelles méthodes / techniques doivent empêcher toute falsification / reproduction non autorisée de la photographie d’identité. Cette thèse propose une méthode de hachage pour l’authentification de photographies d’identité, robuste à l’impression-lecture. Ce travail met ainsi l’accent sur les effets de la numérisation au niveau de hachage. L’algorithme mis au point procède à une réduction de dimension, basée sur l’analyse en composantes indépendantes (ICA). Dans la phase d’apprentissage, le sous-espace de projection est obtenu en appliquant l’ICA puis réduit selon une stratégie de sélection entropique originale. Dans l’étape d’extraction, les coefficients obtenus après projection de l’image d’identité sur le sous-espace sont quantifiés et binarisés pour obtenir la valeur de hachage. L’étude révèle les effets du bruit de balayage intervenant lors de la numérisation des photographies d’identité sur les valeurs de hachage et montre que la méthode proposée est robuste à l’attaque d’impression-lecture. L’approche suivie en se focalisant sur le hachage robuste d’une classe restreinte d’images (d’identité) se distingue des approches classiques qui adressent une image quelconqu