Course Syllabus for

# Signal Separation - Independent Components Signalseparation - oberoende komponenter

## BMEN16F, 7.5 credits

Valid from: Autumn 2019
Decided by: Professor Thomas Johansson
Date of establishment: 2019-06-05

## General Information

Division: Biomedical Engineering
Course type: Course given jointly for second and third cycle
The course is also given at second-cycle level with course code: BMEN15
Teaching language: English

## Aim

The course gives basic knowledge in statistical signal processing and treats the theory of independent and principal components, together with applications in signal separation. The traditional approaches to analyse, filter, compress and separate a combination of signals by means of second order statistics (e.g. correlation based methods) are extended to include higher order statistics (e.g. higher than second order moments). This leads to the concept of independent components in contrast to principal components.

## Goals

Knowledge and Understanding

For a passing grade the doctoral student must

• be able to apply the theory of independent components for modeling of signals and systems
• be able to apply the theory of independent components in the field of signal separation and feature extraction

Competences and Skills

For a passing grade the doctoral student must

• have knowledge in problem formulations of modeling of linear mixtures of signals
• have knowledge in the use of independent components in separation of linear mixtures of signals

Judgement and Approach

For a passing grade the doctoral student must e able to comprehend literature as well as standards in this area

## Course Contents

The following items are treated in the course: linear representation of multivariate data, random vectors and independence, higher order moments, gradients and optimization, learning rules for non-constrained and constrained optimization, estimation theory for signal separation, methods of least-squares and maximum likelihood, information theory, entropy cumulants, definition of PCA and ICA, differences and similarities between PCA and ICA, methods for estimation of ICA: ICA by maximization of non-Gaussianity, ICA by maximum likelihood estimation, ICA by minimization of mutual information, ICA by nonlinear decorrelation and nonlinear PCA. Applications: acoustic signal separation and deconvolution, feature extraction from multivariate data, artifact identification from EEG and MEG, prediction of time series data by using ICA.

## Course Literature

Hyvärinen, A., Karhunen, J. & Oja, E.: Independent Component Analysis. Wiley-Interscience, 2001. ISBN 9780471405405.

## Instruction Details

Types of instruction: Lectures, exercises, project

## Examination Details

Examination formats: Written exam, written report, written assignments. Fulfilled project work and partial tests during the course.
Examiner:

Assumed prior knowledge: ESS040, EITF75 Digital signal processing OR ETI265, EITA50 Signal processing in multimedia OR EITF15 Digital signal processing - theory and applications

## Contact and Other Information

Course coordinator: Frida Sandberg <frida.sandberg@bme.lth.se>
Web page: www.bme.lth.se