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In this paper, we consider the nonlinear Blind Source Separation BSS and independent component analysis (ICA) problems, and especially uniqueness issues, presenting some new results. A fundamental difficulty in the nonlinear BSS problem and even more so in the nonlinear ICA problem is that they are nonunique without a suitable regularization. In this paper, we mainly discuss three different ways for regularizing the solutions, that have been recently explored. © 2003 Elsevier B.V. All rights reserved  

In this paper a new geometrical approach for separating speech signals is presented. This approach can be directly applied to separate more than two speech signals. It is based on clustering the observation points, and then fitting a line (hyper-plane) onto each cluster. The algorithm quality is shown to be improved by using DCT coefficients of speech signals, as opposed to using speech samples. © Springer-Verlag 2004  

In this paper, the problem of single microphone source separation via Nonnegative Matrix Factorization (NMF) by exploiting video information is addressed. Respective audio and video modalities coming from a single human speech usually have similar time changes. It means that changes in one of them usually corresponds to changes in the other one. So it is expected that activation coefficient matrices of their NMF decomposition are similar. Based on this similarity, in this paper the activation coefficient matrix of the video modality is used as an initialization for audio source separation via NMF. In addition, the mentioned similarity is used for post-processing and for clustering the rows... 

In this letter, we compute the variation of the mutual information, resulting from a small variation in its argument. Although the result can be applied in many problems, we consider only one example: the result is used for deriving a new method for blind source separation in linear mixtures. The experimental results emphasize the performance of the resulting algorithm  

In this paper, a new algorithm for blind source separation in convolutive mixtures, based on minimizing the mutual information of the outputs, is proposed. This minimization is done using a recently proposed Minimization-Projection (MP) approach for minimizing mutual information in a parametric model. Since the minimization step of the MP approach is proved to have no local minimum, it is expected that this new algorithm has good convergence behaviours  

Let A be an n × m matrix with m > n, and suppose that the underdetermined linear system As = x admits a sparse solution ∥s 0∥o < 1/2spark(A). Such a sparse solution is unique due to a well-known uniqueness theorem. Suppose now that we have somehow a solution ŝ as an estimation of s0, and suppose that ŝ is only "approximately sparse", that is, many of its components are very small and nearly zero, but not mathematically equal to zero. Is such a solution necessarily close to the true sparsest solution? More generally, is it possible to construct an upper bound on the estimation error ∥ŝ - s 0∥2 without knowing s0? The answer is positive, and in this paper, we construct such a bound based on... 

Digital documents are usually degraded during the scanning process due to the contents of the backside of the scanned manuscript. This is often caused by the show-through effect, i. e. the backside image that interferes with the main front side picture due to the intrinsic transparency of the paper. This phenomenon is one of the degradations that one would like to remove especially in the field of Optical Character Recognition (OCR) or document digitalization which require denoised texts as inputs. In this paper, we first propose a novel and general nonlinear model for canceling the show-through phenomenon. A nonlinear blind source separation algorithm is used for this purpose based on a new... 

This paper deals with blind separation of finite alphabet sources where we have n sources and only one observation. The method is applied directly in time (spatial) domain and no transformation is needed. It follows a two stage procedure. In the first stage the mixing coefficients are estimated, and in the second stage the sources are separated using the estimated mixing coefficients. We also study restrictions of this method and conditions for which its performance is acceptable. Simulation results are presented to show the ability of this method to source separation in images and pulse amplitude modulation (PAM) signals  

A geometric method for separating PNL mixtures, for the case of 2 sources and 2 sensors, has been presented. The main idea is to find compensating nonlinearities to transform the scatter plot of observations to a parallelogram. It then results in a linear mixture which can be separated by any linear source separation algorithm. An indirect result of the paper is another separability proof of PNL mixtures of bounded sources for 2 sources and 2 sensors  

Digital documents are usually degraded during the scanning process due to the printings existing on the backside of the scanning manuscript. This is often caused by the so called show-through effect, the image that interferes with the main picture due to the intrinsic opacity of the paper. This phenomenon is on type of degradation that one would like to remove. In this paper, we propose a novel and general nonlinear model for show-through phenomenon. A nonlinear blind source separation (BSS) algorithm is used for this particular application in a new recursive and extendible structure for compensating show-through. Finally, we introduce a new structure for removing the show-through and the... 

In this paper, a proof is provided to show that Gaussian signals will lose their Gaussianity if they are passed through a polynomial of an order greater than 1. This can help in blind compensation of polynomial nonlinearities on Gaussian sources by forcing the output to follow a Gaussian distribution (the term 'blind' refers to lack of any prior information about the nonlinear function). It may have many applications in different fields of nonlinear signal processing for removing the nonlinearity. Particularly, in nonlinear blind source separation, it can be used as a pre-processing step to transform the problem to a linear one, which is already well studied in the literature. This idea is... 

Using Mutual Information (MI) minimization is very common in Blind Source Separation (BSS). However, it is known that gradient descent approaches may trap in local minima of MI in constrained models. In this paper, it is proposed that this problem may be solved using a 'poor' estimation of the derivative of MI  

In this paper, an adaptive algorithm for blind source separation in linear instantaneous mixtures is proposed, and it is shown to be the optimum version of the EASI algorithm. The algorithm is based on minimization of mutual information of outputs. This minimization is done using adaptive estimation of a recently proposed non-parametric "gradient" for mutual information. © Springer-Verlag 2004  

Blind Source Separation (BSS) is a basic problem in signal processing. In this paper, we present a new method for separating convolutive mixtures based on the minimization of the output mutual information. We also introduce the concept of joint score function, and derive its relationship with marginal score function and independence. The new approach for minimizing the mutual information is very efficient, although limited by multivariate distribution estimations. © Springer-Verlag Berlin Heidelberg 2001  

The electrooculogram (EOG) artifact is one of the main contaminators of electroencephalographic recording (EEG). EOG can make serious problems in results and interpretations of EEG processing. Rejecting contaminated EEG segments result in an unacceptable data loss. Many methods were proposed to correct EOG artifact mainly based on regression and blind source separation (BSS). In this study, we proposed an automatic correction method based on maximum likelihood estimation. The proposed method was applied to our simulated data (real artifact free EEG plus controlled EOG) and results show that this method gives superior performance to Schlögl and SOBI methods  

Blind Source Separation (BSS) is the problem of separating signals which are mixed through an unknown function from a number of observations, without any information about the mixing model. Although it has been mathematically proven that the separation can be done when the mixture is linear, there is not any proof for the separability of nonlinearly mixed signals. Our contribution in this paper is performing nonlinear BSS for sparse sources. It is shown in this case, sources are separable even if the problem is under-determined (the number of observations is less than the number of source signals). However in the most general case (when the nonlinear mixing model can be of any kind and there... 

In this paper, the problem of convolutive source separation via multimodal soft Nonnegative Matrix Co-Factorization (NMCF) is addressed. Different aspects of a phenomenon may be recorded by sensors of different types (e.g., audio and video of human speech), and each of these recorded signals is called a modality. Since the underlying phenomenon of the modalities is the same, they have some similarities. Especially, they usually have similar time changes. It means that changes in one of them usually correspond to changes in the other one. So their active or inactive periods are usually similar. Assuming this similarity, it is expected that the activation coefficient matrices of their... 

Detection of seizure periods in an epileptic patient is an important part of health care. However, due to the variety in types of seizures and location of them, real-time seizure detection is not straight forward. In this paper, we propose a method for seizure detection from EEG signals in datasets which have both generalized and focal seizures. The proposed method is useful in the situations that we have no prior knowledge about the location of the patient's seizure and the pattern of evolution of seizure location. In the proposed method, first, the artifacts are automatically reduced by Blind Source Separation (BSS) methods. Then, the channels are clustered into two clusters. After that,... 

Automated measurement of the intensity of spontaneous facial Action Units (AU) defined by the Facial Action Coding System (FACS) in video sequences is a challenging problem. This paper proposes a person-adaptive methodology for the intensity estimation of spontaneous AUs. We formulate this problem as a source separation problem where we consider the observed AUs as the source signals to be separated from each other and other information given by a sequence of facial images. We first compute an initial estimation of the sources, called observations, using sparse linear regression functions. We then develop and apply a Bayesian source separation method that recruits the prior information of...