No Arabic abstract
Over the last ten years blind source separation (BSS) has become a prominent processing tool in the study of human electroencephalography (EEG). Without relying on head modeling BSS aims at estimating both the waveform and the scalp spatial pattern of the intracranial dipolar current responsible of the observed EEG. In this review we begin by placing the BSS linear instantaneous model of EEG within the framework of brain volume conduction theory. We then review the concept and current practice of BSS based on second-order statistics (SOS) and on higher-order statistics (HOS), the latter better known as independent component analysis (ICA). Using neurophysiological knowledge we consider the fitness of SOS-based and HOS-based methods for the extraction of spontaneous and induced EEG and their separation from extra-cranial artifacts. We then illustrate a general BSS scheme operating in the time-frequency domain using SOS only. The scheme readily extends to further data expansions in order to capture experimental source of variations as well. A simple and efficient implementation based on the approximate joint diagonalization of Fourier cospectral matrices is described (AJDC). We conclude discussing useful aspects of BSS analysis of EEG, including its assumptions and limitations.
Approximate joint diagonalization of a set of matrices provides a powerful framework for numerous statistical signal processing applications. For non-unitary joint diagonalization (NUJD) based on the least-squares (LS) criterion, outliers, also referred to as anomaly or discordant observations, have a negative influence on the performance, since squaring the residuals magnifies the effects of them. To solve this problem, we propose a novel cost function that incorporates the soft decision-directed scheme into the least-squares algorithm and develops an efficient algorithm. The influence of the outliers is mitigated by applying decision-directed weights which are associated with the residual error at each iterative step. Specifically, the mixing matrix is estimated by a modified stationary point method, in which the updating direction is determined based on the linear approximation to the gradient function. Simulation results demonstrate that the proposed algorithm outperforms conventional non-unitary diagonalization algorithms in terms of both convergence performance and robustness to outliers.
This paper presents a computationally efficient approach to blind source separation (BSS) of audio signals, applicable even when there are more sources than microphones (i.e., the underdetermined case). When there are as many sources as microphones (i.e., the determined case), BSS can be performed computationally efficiently by independent component analysis (ICA). Unfortunately, however, ICA is basically inapplicable to the underdetermined case. Another BSS approach using the multichannel Wiener filter (MWF) is applicable even to this case, and encompasses full-rank spatial covariance analysis (FCA) and multichannel non-negative matrix factorization (MNMF). However, these methods require massive numbers of matrix
This paper describes an x-ray microtomographic technique for imaging the three-dimensional structure of the human cerebral cortex. Neurons in the brain constitute a neural circuit as a three-dimensional network. The brain tissue is composed of light elements that give little contrast in a hard x-ray transmission image. The contrast was enhanced by staining neural cells with metal compounds. The obtained structure revealed the microarchitecture of the gray and white matter regions of the frontal cortex, which is responsible for the higher brain functions.
Recently a blind source separation model was suggested for spatial data together with an estimator based on the simultaneous diagonalisation of two scatter matrices. The asymptotic properties of this estimator are derived here and a new estimator, based on the joint diagonalisation of more than two scatter matrices, is proposed. The asymptotic properties and merits of the novel estimator are verified in simulation studies. A real data example illustrates the method.
Recently Lin et al. proposed a method of using the underdetermined BSS (blind source separation) problem to realize image and speech encryption. In this paper, we give a cryptanalysis of this BSS-based encryption and point out that it is not secure against known/chosen-plaintext attack and chosen-ciphertext attack. In addition, there exist some other security defects: low sensitivity to part of the key and the plaintext, a ciphertext-only differential attack, divide-and-conquer (DAC) attack on part of the key. We also discuss the role of BSS in Lin et al.s efforts towards cryptographically secure ciphers.