BLIND SOURCE SEPARATION(BSS)

BLIND SOURCE SEPARATION(BSS)USING INDEPENDENT COMPONENT ANALYSIS (ICA) FAST ICA ALGORITHM

Ajay Mohan M Vandana RajanNikhil Cherian Kurian

1COURTESY Aapo Johannes Hyvarinen

Senior Research Scientist - Helsinki Institute of Information Technology (HIIT), and Dept of Computer Science, University of Helsinki.2SituationCocktail Party Problem 2 recorded time signals x1(t) and x2(t) x1(t) = a11 s1 + a12 s2 (1) x2(t) = a21 s1 + a22 s2 (2)Vector matrix notation( ICA model) x = As (3)

3BSS and ICABSS Blind Source/Signal Separation Source Original signal i.e.; the speaker Blind Very little or No knowledge of mixing matrix.

ICA A method to perform BSS. 4ICA Diagram

5Wave FormsOriginal Source SignalsMixed signals

6Original Source Signals

7Mixed Signals

8Solution Since x = A s, solution can be s = W x (4) where, W is the un mixing matrix.

BUT A is also UNKNOWN!!!!! Thus we go for FAST ICA Algorithm.

9Assumptions made: Statistical Independence of sources.Non - Gaussian distribution of sources.10IndependenceSpeech signals from 2 DIFFERENT speakers Knowledge about one DOESNOT give information about the other.Can be defined using probability densities p(y1,y2) = p(y1) p(y2) (5) Independent Un-correlated

11Non-GaussianConsider the joint pdf of 2 Gaussian variablesp(x1,x2) is given by (1/(2 * pi)) * exponent(-(x1) 2+(x2)2)/2) --- (6)12

Distribution of Gaussian variables Symmetric in nature13

An un symmetric distribution that gives the direction of columns of mixing matrix14Since graphical analysis is difficult for larger dimensions we go for ICA algorithms based on statistical principles.

15FAST ICA ALGORITHM USING MATLAB ( 2011 version )16Step 1 Get some dataHere we used 2 mixed signals as inputsIf there are 2 sources then at least 2 mixtures are neededThese are taken as 2 rows of the matrix x. 17Pre processing of dataMakes data handling easier.Different pre processing steps are done depending upon the application.Here steps 2 and 3 are pre processing steps. 18Step 2 Data Centring This is done solely to simplify the algorithm.Mean is the average across each dimension.Subtract mean from each signal.This produces a data set whose MEAN is ZERO 19Step 3 Enhance the Signal StrengthEach row is divided by its standard deviation.This is done to compress the data.Then the variance of the distribution becomes unity.20Step 4 Covariance matrixCovariance measured between 2 or more data dimensions.Measures how much 2 variables change together.SD and variance single dimensions.

21Step 5 Eigen vectors and Eigen values of Covariance matrixEigen vectors of a matrix are orthogonal.Data can be represented in terms of these orthogonal vectors.Eigen vector with the highest Eigen value is the principle component.Order the vectors by Eigen values highest to lowest. 22Step 6 Whitening Process of making components un-correlated and variance equals unity.Covariance matrix Identity matrix.Eigen value decomposition (EVD) of co-variance matrix.The process of making all the Eigen values same whitening.

23Step 7 FastICA AlgorithmANN based algorithm.Weighted connections are used. One unit algorithm with multiple iteration is implemented. The weights are adjusted till the required convergence is obtained.

24Retrieved Signals I (Under-Sampled)

25Retrieved Signal I (Complete)

26Retrieved Signals II (Under-Sampled)

27Retrieved Signals II (Complete)

28ConclusionRetrieval by estimating signals with expected propertiesApproximation of real time mixing processes Retrieved samples are attenuated Amplitude decreases as distance from source increases.29Future WorkImplementation of Bell-Sojnowski Algorithm & Clustering AlgorithmAdditional De-noising required for practical implementationConsideration of random effects like reflectionsAuditory Scene Analysis for hardware implementation

30ReferencesAapo Hyvarinen, Juha Karhunen, and Erikka Oja Independent Component AnalysisAapo Hyvarinen, and Ella Bingham A fast fixed point Algorithm for Independent Component Analysis of Complex valued signals,G.D.Clifford,Blind Source Separation Principal and Independent Component AnalysisA.J.Bell and T.J.Sejnowski An Information Maximization approach to blind separation and blind deconvlution31THANK YOU !!!32