Project Report for Undergraduate Research Opportunity Program

Title : Blind Source Separation

Supervisor : Dr. Jonathon Chambers

Undergraduate Student: Pamornpol Jinachitra

Department : Electrical and Electronic Engineering

Date : 27^th June – 7^th August 2000

Project Overview

The project involves the theoretical study of blind source separation (BSS) which has been an issue of extensive research in the past few years. A famous example of application is in the cocktail party problem where many people are talking at the same time. The objective of BSS is then to separate the voices of people, detected by some microphones located at different places, one from another, without any prior knowledge of the statistics of the signals. Its other interesting applications include cross-talk removal in multichannel communications, feature extraction and separation of biological signals detected from the brain’s activities. The basic model of the problem is that a number of independent signals are instantaneously mixed together, with noise neglected. This can be represented in matrix form as

x = As

where x, nx1, contains the mixed signals presented at the sensors, s, mx1, contains the original source signal and A, nxm, is a mixing matrix and n ³ m. We then want to find a separating matrix W such that

u = Wx

where u, mx1, contains estimates of the separated signals.

Various algorithms have been proposed to solve the problem. Some were implemented and simulated in Matlab using prescribed mixtures of synthetic data and real speech. In order to be able to assess performance of different algorithms or settings, a performance index was calculated. Some of the results in the case of two sources and mixing matrix are shown below.

Having studied this simple instantaneous model, I extended the area to a more complicated, but yet more realistic, model where now the mixing may have some delays between sources. The more general form of the problem of this kind is when the sources are convolved when mixed. This happens in a real world situation where sound is reflected from the walls of a room many times and hence arrives at the microphones at different times with different amplitudes. An algorithm using a feedback network whose weights are w₁₂ and w₂₁ was implemented and simulated. Some good results after 20,000 iterations are shown below for the case

x₁(n) = s₁(n) + 0.4* s₂(n-D₁₂) D₁₂ = 10

x₂(n) = s₂(n) + 0.8* s₁(n-D₂₁) D₂₁ = 20

This is the area where more research is still needed. I therefore hope to make some contribution in this area as an extension of the work I have already done during the UROP training in the near future.

Personal achievement

· A great deal of learning about the subject which complements well with the study I have already taken as part of my undergraduate studies.

· A proposal for my final year project, entitled “Blind Source Separation for Convolutive Mixtures”.

· Some literature review on the proposed project and some potentially useful experimental results.

· An invaluable experience and learning on conducting a research, especially when I intend to do a Ph.D. and pursue an academic career.

· More familiarity with academic journals.

· A clearer idea of my future study and a possible contribution I could make to the research community.

Supervisor’s benefit

· An assistantship on preparing slides and demonstrations for presentations.

· A summary of some literatures that may be interesting and useful to the current work.

Importance of the bursary

· As the project did not have an industrial sponsorship, the bursary helped ease the cost of living in London to do this interesting project.

· In some cases, it could probably have increased the chance of getting to do the project one really wanted to despite any possible shortage of funding.

Acknowledgement : I would like to thank Dr. Jonathon Chambers for his kind supervision, as well as the teaching and many useful comments and suggestions I received.