Least Dependent Component Analysis Based on Mutual Information

We propose to use precise estimators of mutual information (MI) to find least dependent components in a linearly mixed signal. On the one hand this seems to lead to better blind source separation than with any other presently available algorithm. On the other hand it has the advantage, compared to other implementations of `independent' component analysis (ICA) some of which are based on crude approximations for MI, that the numerical values of the MI can be used for: (i) estimating residual dependencies between the output components; (ii) estimating the reliability of the output, by comparing the pairwise MIs with those of re-mixed components; (iii) clustering the output according to the residual interdependencies. For the MI estimator we use a recently proposed k-nearest neighbor based algorithm. For time sequences we combine this with delay embedding, in order to take into account non-trivial time correlations. After several tests with artificial data, we apply the resulting MILCA (Mutual Information based Least dependent Component Analysis) algorithm to a real-world dataset, the ECG of a pregnant woman. The software implementation of the MILCA algorithm is freely available at http://www.fz-juelich.de/nic/cs/softwareComment: 18 pages, 20 figures, Phys. Rev. E (in press

Dependent Component Analysis for Multi-frame Image Restoration and Enhancement

Abstract Independent component analysis (ICA

Information Theoretic Principles of Universal Discrete Denoising

Today, the internet makes tremendous amounts of data widely available. Often, the same information is behind multiple different available data sets. This lends growing importance to latent variable models that try to learn the hidden information from the available imperfect versions. For example, social media platforms can contain an abundance of pictures of the same person or object, yet all of which are taken from different perspectives. In a simplified scenario, one may consider pictures taken from the same perspective, which are distorted by noise. This latter application allows for a rigorous mathematical treatment, which is the content of this contribution. We apply a recently developed method of dependent component analysis to image denoising when multiple distorted copies of one and the same image are available, each being corrupted by a different and unknown noise process. In a simplified scenario, we assume that the distorted image is corrupted by noise that acts independently on each pixel. We answer completely the question of how to perform optimal denoising, when at least three distorted copies are available: First we define optimality of an algorithm in the presented scenario, and then we describe an aymptotically optimal universal discrete denoising algorithm (UDDA). In the case of binary data and binary symmetric noise, we develop a simplified variant of the algorithm, dubbed BUDDA, which we prove to attain universal denoising uniformly.Comment: 10 pages, 6 figure