ASI - Seminar Project Presentation

Itroduction into Blind Signal Separation and

Preprocessing for BSS Improvement


1. Introduction

[IntroImage] [Motivation] [Problem statement] [Methods] [PCA] [HOS] [FastICA]

original signals

mixed signals

demixed signals


2. Motivation

[IntroImage] [Motivation] [Problem statement] [Methods] [PCA] [HOS] [FastICA]


3. Problem Statement

[IntroImage] [Motivation] [Problem statement] [Methods] [PCA] [HOS] [FastICA]

source signals:
mixed signals:
separated signals:

 

Scalar mixture:
Goal: Matrix W:
Global matrix:

 

Permutation matrix  
Diagonal matrix

 

 

Assumptions:

statistical independence:

5. Methods

[IntroImage] [Motivation] [Problem statement] [Methods] [PCA] [HOS] [FastICA]

Iterationbatchon-line
StatisticsSOSHOS
SOS
PCA - EVD,SVD,NN
GHA
CRLS
Output decorrelation: Chan
Molgedey & Schuster
TDSEP
CoBliSS
HOS
JADE
FastICA
Infomax NN
Cichocki, Amari, Choi: Natural Gradient
Hybrid NN
Spatio-temporal Decorrelation
nonlinear PCA - bigradient
recurrent NN: Jutten&Herault
HybridCDMA NN
FIR matrix: MBLMS/WMBLMS
MBRLS
Smaragdis
SOM

5. PCA

[IntroImage] [Motivation] [Problem statement] [Methods] [PCA] [HOS] [FastICA]

Section about PCA is better to view in pdf format. Paper is available here.

Results of PCA


6. Higher Order Statistics based methods

[IntroImage] [Motivation] [Problem statement] [Methods] [PCA] [HOS] [FastICA]

Methods for BSS can be described by generalized contrast function which is a certain measure of statistical independence/nongaussianity (implies from the Central Limit Theorem). For example:
1. cummulants - kurtosis
2. negentropy,
where
3. approximation bytanh(.), exp(-x2/2)

In section Experiments & Presentations are results of various methods based on HOS.


7. Efficient algorithm for ICA: FastICA

[IntroImage] [Motivation] [Problem statement] [Methods] [PCA] [HOS] [FastICA]

Algorithm is based on approximation of independence measure by contrast function. It is a batch algorithm and uses modified Newton's method for fast separation. The algorithm derivation is available here.

Results of FastICA are also available at Experiments & Presentations.