Sparse Independent Component Analysis with interpolation for Blind Source Separation (original) (raw)
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Sparse Kernel Independent Component Analysis for Blind Source 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).
Blind Source Separation via Independent Component Analysis : Algorithms and Applications
Blind Source Separation (BSS) refers to the process of recovering source signals from a given mixture of unknown source signals were in no prior information about source and mixing methodology is known. Independent Component Analysis (ICA) is widely used BSS technique which allows separation of source components from complex mixture of signals based on certain statistical assumptions. This paper covers up the fundamental concepts of ICA and reviews different algorithms of Independent Component Analysis. In addition, the merits and demerits of each algorithm are outlined. Finally brief description of recent application in ICA is presented.
Semi-blind approaches for source separation and independent component analysis
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.
Sparse component analysis for blind source separation with less sensors than sources
2003
A sparse decomposition approach of observed data matrix is presented in this paper and the approach is then used in blind source separation with less sensors than sources. First, sparse representation (factorization) of a data matrix is discussed. For a given basis matrix, there exist infinite coefficient matrices (solutions) generally such that the data matrix can be represented by the product of the basis matrix and coefficient matrices. However, the sparse solution with minimum 1-norm is unique with probability one, and can be obtained by using linear programming algorithm. The basis matrix can be estimated using gradient type algorithm or Kmeans clustering algorithm. Next, blind source separation is discussed based on sparse factorization approach. The blind separation technique includes two steps, one is to estimate a mixing matrix (basis matrix in the sparse representation), the second is to estimate sources (coefficient matrix). If the sources are sufficiently sparse, blind separation can be carried out directly in the time domain. Otherwise, blind separation can be implemented in time-frequency domain after applying wavelet packet transformation preprocessing to the observed mixtures. Three simulation examples are presented to illustrate the proposed algorithms and reveal algorithms performance. Finally, concluding remarks review the developed approach and state the open problems for further studying.
EFFICIENT ALGORITHM BASED ON BLIND SOURCE SEPARATION INDEPENDENT COMPONENT ANALYSIS USING MATLAB
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.
A COMPARATIVE STUDY OF BLIND SOURCE SEPARATION BASED ON PCA AND ICA
IJCRT, 2022
Blind source separation (BSS) consists of the extraction of individual signals from their mixture using no prior knowledge about their nature. Here, we address the blind separation of audio sources by means of Principal component analysis (PCA) and Independent Component Analysis (ICA), which is a popular method for BSS using the assumption that the original sources are mutually independent. PCA and ICA algorithm working for mixed signals is studied and depicted in this paper.
A fast blind source separation algorithm based on the temporal structure of signals
Neurocomputing, 2014
Classical independent component analysis (ICA) has been reasonably successful; however, the performance and the convergence of the conventional ICA algorithms have reached limitations of further improvement since they utilize only the statistical independency among the sources. For circumventing this situation, in this paper, we incorporate some other kinds of temporal priori information, i.e., the generalized autocorrelation and the nonlinear predictability of each source, and make a convex combination of them to formulate a novel cost function for blind source separation (BSS). With this cost function, a fixed-point BSS algorithm is developed. This algorithm inherits the advantages of the well-known FastICA algorithm of ICA, which converges fast and does not need to choose any learning step sizes. Its higher separation accuracy is verified by numerical experiments. Meanwhile, we also give the consistency analysis and prove convergence properties of the algorithm, which has a (locally) consistent estimator and at least quadratic convergence.
In the linear case statistical independence is a sufficient criterion for performing blind source separation. In the nonlinear case, however, it leaves an ambiguity in the solutions that has to be resolved by additional criteria. Here we argue that temporal slowness complements statistical independence well and that a combination of the two leads to unique solutions of the nonlinear blind source separation problem. The algorithm we present is a combination of second-order Independent Component Analysis and Slow Feature Analysis and is referred to as Independent Slow Feature Analysis. Its performance is demonstrated on nonlinearly mixed music data. We conclude that slowness is indeed a useful complement to statistical independence but that time-delayed second-order moments are only a weak measure of statistical independence.
2004
Our contribution briefly outlines the basics of the well-established technique in data mining, namely the principal component analysis (PCA), and a rapidly emerging novel method, that is, the independent component analysis (ICA). The performance of PCA singular value decomposition-based and stationary linear ICA in blind separation of artificially generated data out of linear mixtures was critically evaluated and compared. All our results outlined the superiority of ICA relative to PCA in faithfully retrieval of the original independent source components.
Blind Source Separation and Independent Component Analysis: A Review
2005
Blind source separation (BSS) and independent component analysis (ICA) are generally based on a wide class of unsupervised learning algorithms and they found potential applications in many areas from engineering to neuroscience. A recent trend in BSS is to consider problems in the framework of matrix factorization or more general signals decomposition with probabilistic generative and tree structured graphical models and exploit a priori knowledge about true nature and structure of latent (hidden) variables or sources such as spatio-temporal decorrelation, statistical independence, sparseness, smoothness or lowest complexity in the sense e.g., of best predictability. The possible goal of such decomposition can be considered as the estimation of sources not necessary statistically independent and parameters of a mixing system or more generally as finding a new reduced or hierarchical and structured representation for the observed (sensor) data that can be interpreted as physically meaningful coding or blind source estimation. The key issue is to find a such transformation or coding (linear or nonlinear) which has true physical meaning and interpretation. We present a review of BSS and ICA, including various algorithms for static and dynamic models and their applications. The paper mainly consists of three parts: