Morphological diversity and source separation

2009 4th International IEEE/EMBS Conference on Neural Engineering, 2009

To remove artifacts from multi-channel Electroencephalography (EEG) data, we propose the use of Generalized Morphological Component Analysis (GMCA). GMCA separates the EEG signals into sources that have different morphological characteristics. Each source is sparse in an overcomplete dictionary, which is constructed using discrete cosine transform, Daubechies wavelet basis and Dirac basis. The sources related to artifacts are then removed. Semi-simulated EEG signals of movement-related potentials trials contaminated by eye-blink and muscle artifacts are used to evaluate the algorithm's performance. The performance of GMCA is compared with those of two other blind source separation algorithms, AMUSE and EFICA. The results demonstrate that GMCA successfully removes artifacts from EEG signals and the resulting distortions in both time and frequency domains are significantly lower than those of the other algorithms.

2008

Abstract:-Independent component analysis is a generative model for observed multivariate data, which are assumed to be mixtures of some unknown latent variables. It is a statistical and computational technique for revealing hidden factors that underlies set of random variable measurements of signals. A common problem faced in the disciplines such as statistics, data analysis, signal processing and neural network is finding a suitable representation of multivariate data.

Independent component analysis is a lively field of research and is being utilized for its potential in statistically independent separation of images. ICA based algorithms has been used to extract interference and mixed images and a very rapid developed statistical method during last few years. So, in this paper an efficient result oriented algorithm for ICA-based blind source separation has been presented. In blind source separation primary goal is to recover all original images using the observed mixtures only. Independent Component Analysis (ICA) is based on higher order statistics aiming at penetrating for the components in the mixed signals that are statistically as independent from each other as achievable.

Journal of Mathematical Imaging and Vision, 2008

Over the last decade, overcomplete dictionaries and the very sparse signal representations they make possible, have raised an intense interest from signal processing theory. In a wide range of signal processing problems, sparsity has been a crucial property leading to high performance. As multichannel data are of growing interest, it seems essential to devise sparsity-based tools accounting for such specific multichannel data. Sparsity has proved its efficiency in a wide range of inverse problems. Hereafter, we address some multichannel inverse problems issues such as multichannel morphological component separation and inpainting from the perspective of sparse representation. In this paper, we introduce a new sparsity-based multichannel analysis tool coined multichannel Morphological Component Analysis (mMCA). This new framework focuses on multichannel morphological diversity to better represent multichannel data. This paper presents conditions under which the mMCA converges and recovers the sparse multichannel representation. Several experiments are presented to demonstrate the applicability of our approach on a set of multichannel inverse problems such as morphological component decomposition and inpainting.

2007

In this article we investigate the performance of the ICA algorithm AMUSE when applied to images contaminated by noise. The classes of noise we are using have gaussian, multiplicative and impulsive distributions. We find that AMUSE copes surprisingly well with the different types of noise, including multiplicative noise.

Advances in Imaging and Electron Physics, 2008

Over the last few years, the development of multi-channel sensors motivated interest in methods for the coherent processing of multivariate data. Some specific issues have already been addressed as testified by the wide literature on the so-called blind source separation (BSS) problem. In this context, as clearly emphasized by previous work, it is fundamental that the sources to be retrieved present some quantitatively measurable diversity. Recently, sparsity and morphological diversity have emerged as a novel and effective source of diversity for BSS. We give here some essential insights into the use of sparsity in source separation and we outline the essential role of morphological diversity as being a source of diversity or contrast between the sources. This paper overviews a sparsity-based BSS method coined Generalized Morphological Component Analysis (GMCA) that takes advantages of both morphological diversity and sparsity, using recent sparse overcomplete or redundant signal representations. GMCA is a fast and efficient blind source separation method. In remote sensing applications, the specificity of hyperspectral data should be accounted for. We extend the proposed GMCA framework to deal with hyperspectral data. In a general framework, GMCA provides a basis for multivariate data analysis in the scope of a wide range of classical multivariate data restorate. Numerical results are given in color image denoising and inpainting. Finally, GMCA is applied to the simulated ESA/Planck data. It is shown to give effective astrophysical component separation.

2008

We address the problem of Blind Source Separation (BSS) of superimposed signals in situations where one signal has constant or slowly varying intensities at some consecutive locations and at the corresponding locations the other signal has highly varying intensities. Independent Component Analysis (ICA) is a major technique for Blind Source Separation and the existing ICA algorithms fail to estimate the original intensities in the stated situation. We combine the advantages of existing sparse methods and Kernel ICA in our technique, by proposing wavelet packet based sparse decomposition of signals prior to the application of Kernel ICA. Simulations and experimental results illustrate the effectiveness and accuracy of the proposed approach. The approach is general in the way that it can be tailored and applied to a wide range of BSS problems concerning one-dimensional signals and images (two-dimensional signals).

2009 2nd International Conference on Computer, Control and Communication, 2009

The separation of a superposition of multiple signals is accomplished by taking into account the structure of the mixing process and by making assumptions about the sources. By assuming that the sources can be represented sparsely in a given basis, recent research has demonstrated that better results can be obtained. In this paper, we will show that increasing the size of mixture of signals by estimating new data points using the technique of interpolation can be used to increase the accuracy of Blind Source Separation (BSS) methods. We propose a four step BSS technique for instantaneous case which increases the accuracy of the sparse BSS methods. These steps include Interpolation, Sparse Decomposition, Independent Component Analysis (ICA) algorithm, and Downsampling. The idea is to use the combination of interpolation and sparsing as preprocessing for ICA. Although the method works for both one dimensional and two dimensional signals, it is best suitable for two dimensional signals like images. Results of the proposed method on one dimensional and two dimensional signals have been presented.

2006

This paper is a survey of semi-blind source separation approaches. Since Gaussian iid signals are not separable, simplest priors suggest to assume non Gaussian iid signals, or Gaussian non iid signals. Other priors can also been used, for instance discrete or bounded sources, positivity, etc. Although providing a generic framework for semi-blind source separation, Sparse Component Analysis and Bayesian ICA will just sketched in this paper, since two other survey papers develop in depth these approaches.

Image fusion can produce a single image that describes the scene better than the individual source image. One of the keys to image fusion algorithm is how to effectively and completely represent the source images. Morphological component analysis (MCA) believes that an image contains structures with different spatial morphologies and can be accordingly modeled as a superposition of cartoon and texture components, and that the sparse representations of these components can be obtained by some specific decomposition algorithms which exploit the structured dictionary. Compared with the traditional multiscale decomposition, which has been successfully applied to pixel-level image fusion, MCA employs the morphological diversity of an image and provides more complete representation for an image. Taking advantage of this property, we propose a multi-component fusion method for multi-source images in this paper. In our method, source images are separated into cartoon and texture components, and essential fusion takes place on the representation coefficients of these two components. Our fusion scheme is verified on three kinds of images and compared with six single-component fusion methods. According to the visual perceptions and objective evaluations on the fused results, our method can produce better fused images in our experiments, compared with other single-component fusion methods.