| Paper: | MLSP-L2.5 | ||
| Session: | Blind Source Separation | ||
| Time: | Friday, May 21, 14:20 - 14:40 | ||
| Presentation: | Lecture | ||
| Topic: | Machine Learning for Signal Processing: Blind Signal Separation and Independent Component Analysis | ||
| Title: | BLIND SOURCE SEPARATION AND SPARSE COMPONENT ANALYSIS OF OVERCOMPLETE MIXTURES | ||
| Authors: | Pando Georgiev; RIKEN, BSI | ||
| Fabian Theis; RIKEN, BSI, Japan / University of Regensburg | |||
| Andrzej Cichocki; RIKEN, BSI | |||
| Abstract: | We formulate conditions (k-SCA-conditions) under which we canrepresent a given $(m\times N)$-matrix $\X$ (data set)uniquely (up to scaling and permutation)as a multiplication of $m\times n$ and $n\times N$ matrices $\A$ and $\SS$ (often called mixing matrix or {\it dictionary} andsource matrix, respectively), such that $\SS$ is {\it sparse of level $n-m+k$} in sense that each column of $\SS$ has at least $n-m+k$ zero elements.We call this the {\it k-Sparse Component Analysis} problem (k-SCA).Conditions on a matrix $\SS$ are presented such that %for any matrix $\A$,the k-SCA-conditions are satisfied for the matrix $\X=\A\SS$, where $\A$ is an arbitrary matrix from some class.This is the {\it Blind Source Separation} problem and the above conditions are called {\it identifiability conditions}. We present two new algorithms: for matrix identification (under k-SCA-conditions), and for source recovery (under identifiability conditions).The methods are illustrated with examples, showing good separation of the high-frequency part of images afterappropriate sparsification. | ||
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