Course syllabus

# Signalseparation - oberoende komponenter Signal Separation - Independent Components

## BMEN15, 7,5 credits, A (Second Cycle)

Valid for: 2020/21
Decided by: PLED BME
Date of Decision: 2020-03-24

## General Information

Elective for: BME5-sbh, C4, D4-ssr, E4-ss, E4-mt, E4-bg, F4, F4-ss, MWIR2, Pi4, MMSR2
Language of instruction: The course will be given in 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.

## Learning outcomes

Knowledge and understanding
For a passing grade the 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 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 student must

• be able to comprehend literature as well as standards in this area

## 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.

## Examination details

Grading scale: TH - (U,3,4,5) - (Fail, Three, Four, Five)
Assessment: Written exam, fulfilled laboratory work and partial tests during the course.

The examiner, in consultation with Disability Support Services, may deviate from the regular form of examination in order to provide a permanently disabled student with a form of examination equivalent to that of a student without a disability.

Parts
Code: 0119. Name: Written Exam.
Credits: 6. Grading scale: TH. Assessment: Written exam
Code: 0219. Name: Laboratory Work.
Credits: 1,5. Grading scale: UG. Assessment: Approved Laboratory work