Extracting individual contributions from their mixture: a blind source separation approach, with examples from space and laboratory plasmas

Multipoint or multichannel observations in plasmas can frequently be modelled as an instantaneous mixture of contributions (waves, emissions, ...) of different origins. Recovering the individual sources from their mixture then becomes one of the key objectives. However, unless the underlying mixing processes are well known, these situations lead to heavily underdetermined problems. Blind source separation aims at disentangling such mixtures with the least possible prior information on the sources and their mixing processes. Several powerful approaches have recently been developed, which can often provide new or deeper insight into the underlying physics. This tutorial paper briefly discusses some possible applications of blind source separation to the field of plasma physics, in which this concept is still barely known. Two examples are given. The first one shows how concurrent processes in the dynamical response of the electron temperature in a tokamak can be separated. The second example deals with solar spectral imaging in the Extreme UV and shows how empirical temperature maps can be built.Comment: expanded version of an article to appear in Contributions to Plasma Physics (2010

Artifact removal and brain rhythm decomposition for eeg signal using wavelet approach

This recent study introduces and discusses briefly the use of wavelet approach in removing the artifacts and extraction of features for electroencephalography (EEG) signal. Many of new approaches have been discovered by the researcher for processing the EEG signal. Generally, the EEG signal processing can be divided into pre-processing and postprocessing. The aim of processing is to remove the unwanted signal and to extract important features from the signal. However, the selections of non-suitable approach affect the actual result and wasting the time and energy. Wavelet is among the effective approach that can be used for processing the biomedical signal. The wavelet approach can be performed in MATLAB toolbox or by coding, that require a simple and basic command. In this paper, the application of wavelet approach for EEG signal processing is introduced. Moreover, this paper also discusses the effect of using db3 mother wavelet with 5th decomposition level of stationary wavelet transform and db4 mother wavelet with 7th decomposition level of discrete wavelet transform in removing the noise and decomposing of the brain rhythm. Besides, the simulation result are also provided for better configuration

Phase Harmonic Correlations and Convolutional Neural Networks

A major issue in harmonic analysis is to capture the phase dependence of frequency representations, which carries important signal properties. It seems that convolutional neural networks have found a way. Over time-series and images, convolutional networks often learn a first layer of filters which are well localized in the frequency domain, with different phases. We show that a rectifier then acts as a filter on the phase of the resulting coefficients. It computes signal descriptors which are local in space, frequency and phase. The non-linear phase filter becomes a multiplicative operator over phase harmonics computed with a Fourier transform along the phase. We prove that it defines a bi-Lipschitz and invertible representation. The correlations of phase harmonics coefficients characterise coherent structures from their phase dependence across frequencies. For wavelet filters, we show numerically that signals having sparse wavelet coefficients can be recovered from few phase harmonic correlations, which provide a compressive representationComment: 26 pages, 8 figure

Wavelet Image Restoration Using Multifractal Priors

Bayesian image restoration has had a long history of successful application but one of the limitations that has prevented more widespread use is that the methods are generally computationally intensive. The authors recently addressed this issue by developing a method that performs the image enhancement in an orthogonal space (Fourier space in that case) which effectively transforms the problem from a large multivariate optimization problem to a set of smaller independent univariate optimization problems. The current paper extends these methods to analysis in another orthogonal basis, wavelets. While still providing the computational efficiency obtained with the original method in Fourier space, this extension allows more flexibility in adapting to local properties of the images, as well as capitalizing on the long history of developments for wavelet shrinkage methods. In addition, wavelet methods, including empirical Bayes specific methods, have recently been developed to effectively capture multifractal properties of images. An extension of these methods is utilized to enhance the recovery of textural characteristics of the underlying image. These enhancements should be beneficial in characterizing textural differences such as those occurring in medical images of diseased and healthy tissues. The Bayesian framework defined in the space of wavelets provides a flexible model that is easily extended to a variety of imaging contexts.Comment: 19 pages, 4 figure