direction of arrival based spatial covariance model for

Direction ofArrival Based

SpatialCovarianceModel For

Blind SourceSeparation[1]

BadriPatro,GokulKrishnan &

Phani Reddy

Introduction

ProblemStatement

literatureSurvey

Matrixfactorization

Back GroundWork

Source MixingModels

SignalRepresentation

ConvolutiveMixing Model inSpatialCovarianceDomain

ProposedMethod

Basic Idea

DoA Kernels

Time-difference ofArrival(TDoA)

Superpositionof DoA Kernels

CNMF Modelfor SCMObservations

CNMF ModelAlgo

ReconstructionandClustering

Direction ofWeightsClustering

Reference

Direction of Arrival Based Spatial CovarianceModel For Blind Source Separation[1]

Badri Patro,Gokul Krishnan & Phani Reddy

EE627A: Project Presentation

Guidance: Prof. Rajesh M. HegdeIndian Institute of Technology, Kanpur

April 10, 2016

Badri, Gokul and Phani DOA based SCM for BSS April 10, 2016 1 / 29

Direction ofArrival Based

SpatialCovarianceModel For

Blind SourceSeparation[1]

BadriPatro,GokulKrishnan &

Phani Reddy

Introduction

ProblemStatement

literatureSurvey

Matrixfactorization

Back GroundWork

Source MixingModels

SignalRepresentation

ConvolutiveMixing Model inSpatialCovarianceDomain

ProposedMethod

Basic Idea

DoA Kernels

Time-difference ofArrival(TDoA)

Superpositionof DoA Kernels

CNMF Modelfor SCMObservations

CNMF ModelAlgo

ReconstructionandClustering

Direction ofWeightsClustering

Reference

Table of contents

1 IntroductionProblem Statementliterature Survey

Matrix factorization

2 Back Ground WorkSource Mixing ModelsSignal RepresentationConvolutive Mixing Model in Spatial Covariance Domain

3 Proposed MethodBasic IdeaDoA Kernels

Time-difference of Arrival(TDoA)Superposition of DoA Kernels

CNMF Model for SCM ObservationsCNMF Model Algo

4 Reconstruction and ClusteringDirection of Weights Clustering

5 Reference

Badri, Gokul and Phani DOA based SCM for BSS April 10, 2016 2 / 29

Direction ofArrival Based

SpatialCovarianceModel For

Blind SourceSeparation[1]

BadriPatro,GokulKrishnan &

Phani Reddy

Introduction

ProblemStatement

literatureSurvey

Matrixfactorization

Back GroundWork

Source MixingModels

SignalRepresentation

ConvolutiveMixing Model inSpatialCovarianceDomain

ProposedMethod

Basic Idea

DoA Kernels

Time-difference ofArrival(TDoA)

Superpositionof DoA Kernels

CNMF Modelfor SCMObservations

CNMF ModelAlgo

ReconstructionandClustering

Direction ofWeightsClustering

Reference

Introduction Problem Statement

Problem Statement

Problem Statement

This presentation will address problem of sourceseparation from multichannel microphone array.Given a mixture of sound signal received from multiplesource and multiple microphone.

our task is to separate out different sources from mixturesignal.

Ex. Given a mixture of sound signal received from 2source and 2 microphone.

our task is to separate out 2 sources from mixture signal.

Badri, Gokul and Phani DOA based SCM for BSS April 10, 2016 3 / 29

Direction ofArrival Based

SpatialCovarianceModel For

Blind SourceSeparation[1]

BadriPatro,GokulKrishnan &

Phani Reddy

Introduction

ProblemStatement

literatureSurvey

Matrixfactorization

Back GroundWork

Source MixingModels

SignalRepresentation

ConvolutiveMixing Model inSpatialCovarianceDomain

ProposedMethod

Basic Idea

DoA Kernels

Time-difference ofArrival(TDoA)

Superpositionof DoA Kernels

CNMF Modelfor SCMObservations

CNMF ModelAlgo

ReconstructionandClustering

Direction ofWeightsClustering

Reference

Introduction Problem Statement

Problem Statement

Problem Statement

This presentation will address problem of sourceseparation from multichannel microphone array.Given a mixture of sound signal received from multiplesource and multiple microphone.

our task is to separate out different sources from mixturesignal.

Ex. Given a mixture of sound signal received from 2source and 2 microphone.

our task is to separate out 2 sources from mixture signal.

Badri, Gokul and Phani DOA based SCM for BSS April 10, 2016 3 / 29

Direction ofArrival Based

SpatialCovarianceModel For

Blind SourceSeparation[1]

BadriPatro,GokulKrishnan &

Phani Reddy

Introduction

ProblemStatement

literatureSurvey

Matrixfactorization

Back GroundWork

Source MixingModels

SignalRepresentation

ConvolutiveMixing Model inSpatialCovarianceDomain

ProposedMethod

Basic Idea

DoA Kernels

Time-difference ofArrival(TDoA)

Superpositionof DoA Kernels

CNMF Modelfor SCMObservations

CNMF ModelAlgo

ReconstructionandClustering

Direction ofWeightsClustering

Reference

Introduction Problem Statement

Problem Statement

Problem Statement

This presentation will address problem of sourceseparation from multichannel microphone array.Given a mixture of sound signal received from multiplesource and multiple microphone.

our task is to separate out different sources from mixturesignal.

Ex. Given a mixture of sound signal received from 2source and 2 microphone.

our task is to separate out 2 sources from mixture signal.

Badri, Gokul and Phani DOA based SCM for BSS April 10, 2016 3 / 29

Direction ofArrival Based

SpatialCovarianceModel For

Blind SourceSeparation[1]

BadriPatro,GokulKrishnan &

Phani Reddy

Introduction

ProblemStatement

literatureSurvey

Matrixfactorization

Back GroundWork

Source MixingModels

SignalRepresentation

ConvolutiveMixing Model inSpatialCovarianceDomain

ProposedMethod

Basic Idea

DoA Kernels

Time-difference ofArrival(TDoA)

Superpositionof DoA Kernels

CNMF Modelfor SCMObservations

CNMF ModelAlgo

ReconstructionandClustering

Direction ofWeightsClustering

Reference

Introduction Problem Statement

Problem Statement

Problem Statement

This presentation will address problem of sourceseparation from multichannel microphone array.Given a mixture of sound signal received from multiplesource and multiple microphone.

our task is to separate out different sources from mixturesignal.

Ex. Given a mixture of sound signal received from 2source and 2 microphone.

our task is to separate out 2 sources from mixture signal.

Badri, Gokul and Phani DOA based SCM for BSS April 10, 2016 3 / 29

Direction ofArrival Based

SpatialCovarianceModel For

Blind SourceSeparation[1]

BadriPatro,GokulKrishnan &

Phani Reddy

Introduction

ProblemStatement

literatureSurvey

Matrixfactorization

Back GroundWork

Source MixingModels

SignalRepresentation

ConvolutiveMixing Model inSpatialCovarianceDomain

ProposedMethod

Basic Idea

DoA Kernels

Time-difference ofArrival(TDoA)

Superpositionof DoA Kernels

CNMF Modelfor SCMObservations

CNMF ModelAlgo

ReconstructionandClustering

Direction ofWeightsClustering

Reference

Introduction Problem Statement

Problem Statement

Problem Statement

This presentation will address problem of sourceseparation from multichannel microphone array.Given a mixture of sound signal received from multiplesource and multiple microphone.

our task is to separate out different sources from mixturesignal.

Ex. Given a mixture of sound signal received from 2source and 2 microphone.

our task is to separate out 2 sources from mixture signal.

Badri, Gokul and Phani DOA based SCM for BSS April 10, 2016 3 / 29

Direction ofArrival Based

SpatialCovarianceModel For

Blind SourceSeparation[1]

BadriPatro,GokulKrishnan &

Phani Reddy

Introduction

ProblemStatement

literatureSurvey

Matrixfactorization

Back GroundWork

Source MixingModels

SignalRepresentation

ConvolutiveMixing Model inSpatialCovarianceDomain

ProposedMethod

Basic Idea

DoA Kernels

Time-difference ofArrival(TDoA)

Superpositionof DoA Kernels

CNMF Modelfor SCMObservations

CNMF ModelAlgo

ReconstructionandClustering

Direction ofWeightsClustering

Reference

Introduction Problem Statement

Problem Statement

Problem Statement

This presentation will address problem of sourceseparation from multichannel microphone array.Given a mixture of sound signal received from multiplesource and multiple microphone.

our task is to separate out different sources from mixturesignal.

Ex. Given a mixture of sound signal received from 2source and 2 microphone.

our task is to separate out 2 sources from mixture signal.

Badri, Gokul and Phani DOA based SCM for BSS April 10, 2016 3 / 29

Direction ofArrival Based

SpatialCovarianceModel For

Blind SourceSeparation[1]

BadriPatro,GokulKrishnan &

Phani Reddy

Introduction

ProblemStatement

literatureSurvey

Matrixfactorization

Back GroundWork

Source MixingModels

SignalRepresentation

ConvolutiveMixing Model inSpatialCovarianceDomain

ProposedMethod

Basic Idea

DoA Kernels

Time-difference ofArrival(TDoA)

Superpositionof DoA Kernels

CNMF Modelfor SCMObservations

CNMF ModelAlgo

ReconstructionandClustering

Direction ofWeightsClustering

Reference

Introduction Problem Statement

Problem Statement

Problem Statement

This presentation will address problem of sourceseparation from multichannel microphone array.Given a mixture of sound signal received from multiplesource and multiple microphone.

our task is to separate out different sources from mixturesignal.

Ex. Given a mixture of sound signal received from 2source and 2 microphone.

our task is to separate out 2 sources from mixture signal.

Badri, Gokul and Phani DOA based SCM for BSS April 10, 2016 3 / 29

Direction ofArrival Based

SpatialCovarianceModel For

Blind SourceSeparation[1]

BadriPatro,GokulKrishnan &

Phani Reddy

Introduction

ProblemStatement

literatureSurvey

Matrixfactorization

Back GroundWork

Source MixingModels

SignalRepresentation

ConvolutiveMixing Model inSpatialCovarianceDomain

ProposedMethod

Basic Idea

DoA Kernels

Time-difference ofArrival(TDoA)

Superpositionof DoA Kernels

CNMF Modelfor SCMObservations

CNMF ModelAlgo

ReconstructionandClustering

Direction ofWeightsClustering

Reference

Introduction Problem Statement

Problem Statement

Problem Statement

This presentation will address problem of sourceseparation from multichannel microphone array.Given a mixture of sound signal received from multiplesource and multiple microphone.

our task is to separate out different sources from mixturesignal.

Ex. Given a mixture of sound signal received from 2source and 2 microphone.

our task is to separate out 2 sources from mixture signal.

Badri, Gokul and Phani DOA based SCM for BSS April 10, 2016 3 / 29

Direction ofArrival Based

SpatialCovarianceModel For

Blind SourceSeparation[1]

BadriPatro,GokulKrishnan &

Phani Reddy

Introduction

ProblemStatement

literatureSurvey

Matrixfactorization

Back GroundWork

Source MixingModels

SignalRepresentation

ConvolutiveMixing Model inSpatialCovarianceDomain

ProposedMethod

Basic Idea

DoA Kernels

Time-difference ofArrival(TDoA)

Superpositionof DoA Kernels

CNMF Modelfor SCMObservations

CNMF ModelAlgo

ReconstructionandClustering

Direction ofWeightsClustering

Reference

Introduction Problem Statement

Problem Statement

Problem Statement

This presentation will address problem of sourceseparation from multichannel microphone array.Given a mixture of sound signal received from multiplesource and multiple microphone.

our task is to separate out different sources from mixturesignal.

Ex. Given a mixture of sound signal received from 2source and 2 microphone.

our task is to separate out 2 sources from mixture signal.

Badri, Gokul and Phani DOA based SCM for BSS April 10, 2016 3 / 29

Direction ofArrival Based

SpatialCovarianceModel For

Blind SourceSeparation[1]

BadriPatro,GokulKrishnan &

Phani Reddy

Introduction

ProblemStatement

literatureSurvey

Matrixfactorization

Back GroundWork

Source MixingModels

SignalRepresentation

ConvolutiveMixing Model inSpatialCovarianceDomain

ProposedMethod

Basic Idea

DoA Kernels

Time-difference ofArrival(TDoA)

Superpositionof DoA Kernels

CNMF Modelfor SCMObservations

CNMF ModelAlgo

ReconstructionandClustering

Direction ofWeightsClustering

Reference

Introduction Problem Statement

BSS(@Clifford)

BSS(@Clifford)

Badri, Gokul and Phani DOA based SCM for BSS April 10, 2016 4 / 29

Direction ofArrival Based

SpatialCovarianceModel For

Blind SourceSeparation[1]

BadriPatro,GokulKrishnan &

Phani Reddy

Introduction

ProblemStatement

literatureSurvey

Matrixfactorization

Back GroundWork

Source MixingModels

SignalRepresentation

ConvolutiveMixing Model inSpatialCovarianceDomain

ProposedMethod

Basic Idea

DoA Kernels

Time-difference ofArrival(TDoA)

Superpositionof DoA Kernels

CNMF Modelfor SCMObservations

CNMF ModelAlgo

ReconstructionandClustering

Direction ofWeightsClustering

Reference

Introduction literature Survey

ICA(Sawada et al.,2004)[5] and (Hyvrinen etal.,2001)[6]*1

frequency-domain BSS involves a permutationproblem:

the permutation ambiguity of ICA in each frequency binshould be aligned so that a separated signal in thetime-domain contains frequency components of the samesource signal.

1These are ref No of My cited paperBadri, Gokul and Phani DOA based SCM for BSS April 10, 2016 5 / 29

Direction ofArrival Based

SpatialCovarianceModel For

Blind SourceSeparation[1]

BadriPatro,GokulKrishnan &

Phani Reddy

Introduction

ProblemStatement

literatureSurvey

Matrixfactorization

Back GroundWork

Source MixingModels

SignalRepresentation

ConvolutiveMixing Model inSpatialCovarianceDomain

ProposedMethod

Basic Idea

DoA Kernels

Time-difference ofArrival(TDoA)

Superpositionof DoA Kernels

CNMF Modelfor SCMObservations

CNMF ModelAlgo

ReconstructionandClustering

Direction ofWeightsClustering

Reference

Introduction literature Survey

DOA(Ikram et al.)[7]and(Nesta et al.)[9]*1

Source permutation is usually solved based on timedifference of arrival (TDoA) interpretation of ICAmixing parameters.

Phase differences become ambiguous when thefrequency exceeds the spatial aliasing limit, whichcorresponds to a wavelength greater than half of themicrophone spacing.

As a result, the TDoAs cannot be directly utilized insolving the permutation problem for high frequencies.

TDoA with the help of DUET [10] and binwiseclustering [11].

1These are ref No of My cited paperBadri, Gokul and Phani DOA based SCM for BSS April 10, 2016 6 / 29

Direction ofArrival Based

SpatialCovarianceModel For

Blind SourceSeparation[1]

BadriPatro,GokulKrishnan &

Phani Reddy

Introduction

ProblemStatement

literatureSurvey

Matrixfactorization

Back GroundWork

Source MixingModels

SignalRepresentation

ConvolutiveMixing Model inSpatialCovarianceDomain

ProposedMethod

Basic Idea

DoA Kernels

Time-difference ofArrival(TDoA)

Superpositionof DoA Kernels

CNMF Modelfor SCMObservations

CNMF ModelAlgo

ReconstructionandClustering

Direction ofWeightsClustering

Reference

Introduction literature Survey

DOA(Ikram et al.)[7]and(Nesta et al.)[9]*1

Source permutation is usually solved based on timedifference of arrival (TDoA) interpretation of ICAmixing parameters.

Phase differences become ambiguous when thefrequency exceeds the spatial aliasing limit, whichcorresponds to a wavelength greater than half of themicrophone spacing.

As a result, the TDoAs cannot be directly utilized insolving the permutation problem for high frequencies.

TDoA with the help of DUET [10] and binwiseclustering [11].

1These are ref No of My cited paperBadri, Gokul and Phani DOA based SCM for BSS April 10, 2016 6 / 29

Direction ofArrival Based

SpatialCovarianceModel For

Blind SourceSeparation[1]

BadriPatro,GokulKrishnan &

Phani Reddy

Introduction

ProblemStatement

literatureSurvey

Matrixfactorization

Back GroundWork

Source MixingModels

SignalRepresentation

ConvolutiveMixing Model inSpatialCovarianceDomain

ProposedMethod

Basic Idea

DoA Kernels

Time-difference ofArrival(TDoA)

Superpositionof DoA Kernels

CNMF Modelfor SCMObservations

CNMF ModelAlgo

ReconstructionandClustering

Direction ofWeightsClustering

Reference

Introduction literature Survey

DOA(Ikram et al.)[7]and(Nesta et al.)[9]*1

Source permutation is usually solved based on timedifference of arrival (TDoA) interpretation of ICAmixing parameters.

Phase differences become ambiguous when thefrequency exceeds the spatial aliasing limit, whichcorresponds to a wavelength greater than half of themicrophone spacing.

As a result, the TDoAs cannot be directly utilized insolving the permutation problem for high frequencies.

TDoA with the help of DUET [10] and binwiseclustering [11].

1These are ref No of My cited paperBadri, Gokul and Phani DOA based SCM for BSS April 10, 2016 6 / 29

Direction ofArrival Based

SpatialCovarianceModel For

Blind SourceSeparation[1]

BadriPatro,GokulKrishnan &

Phani Reddy

Introduction

ProblemStatement

literatureSurvey

Matrixfactorization

Back GroundWork

Source MixingModels

SignalRepresentation

ConvolutiveMixing Model inSpatialCovarianceDomain

ProposedMethod

Basic Idea

DoA Kernels

Time-difference ofArrival(TDoA)

Superpositionof DoA Kernels

CNMF Modelfor SCMObservations

CNMF ModelAlgo

ReconstructionandClustering

Direction ofWeightsClustering

Reference

Introduction literature Survey

DOA(Ikram et al.)[7]and(Nesta et al.)[9]*1

Source permutation is usually solved based on timedifference of arrival (TDoA) interpretation of ICAmixing parameters.

Phase differences become ambiguous when thefrequency exceeds the spatial aliasing limit, whichcorresponds to a wavelength greater than half of themicrophone spacing.

As a result, the TDoAs cannot be directly utilized insolving the permutation problem for high frequencies.

TDoA with the help of DUET [10] and binwiseclustering [11].

1These are ref No of My cited paperBadri, Gokul and Phani DOA based SCM for BSS April 10, 2016 6 / 29

Direction ofArrival Based

SpatialCovarianceModel For

Blind SourceSeparation[1]

BadriPatro,GokulKrishnan &

Phani Reddy

Introduction

ProblemStatement

literatureSurvey

Matrixfactorization

Back GroundWork

Source MixingModels

SignalRepresentation

ConvolutiveMixing Model inSpatialCovarianceDomain

ProposedMethod

Basic Idea

DoA Kernels

Time-difference ofArrival(TDoA)

Superpositionof DoA Kernels

CNMF Modelfor SCMObservations

CNMF ModelAlgo

ReconstructionandClustering

Direction ofWeightsClustering

Reference

Introduction literature Survey

PCA and SVD (@Iyad Batal)

Badri, Gokul and Phani DOA based SCM for BSS April 10, 2016 7 / 29

Direction ofArrival Based

SpatialCovarianceModel For

Blind SourceSeparation[1]

BadriPatro,GokulKrishnan &

Phani Reddy

Introduction

ProblemStatement

literatureSurvey

Matrixfactorization

Back GroundWork

Source MixingModels

SignalRepresentation

ConvolutiveMixing Model inSpatialCovarianceDomain

ProposedMethod

Basic Idea

DoA Kernels

Time-difference ofArrival(TDoA)

Superpositionof DoA Kernels

CNMF Modelfor SCMObservations

CNMF ModelAlgo

ReconstructionandClustering

Direction ofWeightsClustering

Reference

Introduction literature Survey

What can matrix represent

What can matrix represent

System of equations

User rating matrix

ImageMatrix structure in graph theory

Adjacent matrixDistance matrix

Badri, Gokul and Phani DOA based SCM for BSS April 10, 2016 8 / 29

Direction ofArrival Based

SpatialCovarianceModel For

Blind SourceSeparation[1]

BadriPatro,GokulKrishnan &

Phani Reddy

Introduction

ProblemStatement

literatureSurvey

Matrixfactorization

Back GroundWork

Source MixingModels

SignalRepresentation

ConvolutiveMixing Model inSpatialCovarianceDomain

ProposedMethod

Basic Idea

DoA Kernels

Time-difference ofArrival(TDoA)

Superpositionof DoA Kernels

CNMF Modelfor SCMObservations

CNMF ModelAlgo

ReconstructionandClustering

Direction ofWeightsClustering

Reference

Introduction literature Survey

What can matrix represent

What can matrix represent

System of equations

User rating matrix

ImageMatrix structure in graph theory

Adjacent matrixDistance matrix

Badri, Gokul and Phani DOA based SCM for BSS April 10, 2016 8 / 29

Direction ofArrival Based

SpatialCovarianceModel For

Blind SourceSeparation[1]

BadriPatro,GokulKrishnan &

Phani Reddy

Introduction

ProblemStatement

literatureSurvey

Matrixfactorization

Back GroundWork

Source MixingModels

SignalRepresentation

ConvolutiveMixing Model inSpatialCovarianceDomain

ProposedMethod

Basic Idea

DoA Kernels

Time-difference ofArrival(TDoA)

Superpositionof DoA Kernels

CNMF Modelfor SCMObservations

CNMF ModelAlgo

ReconstructionandClustering

Direction ofWeightsClustering

Reference

Introduction literature Survey

What can matrix represent

What can matrix represent

System of equations

User rating matrix

ImageMatrix structure in graph theory

Adjacent matrixDistance matrix

Badri, Gokul and Phani DOA based SCM for BSS April 10, 2016 8 / 29

Direction ofArrival Based

SpatialCovarianceModel For

Blind SourceSeparation[1]

BadriPatro,GokulKrishnan &

Phani Reddy

Introduction

ProblemStatement

literatureSurvey

Matrixfactorization

Back GroundWork

Source MixingModels

SignalRepresentation

ConvolutiveMixing Model inSpatialCovarianceDomain

ProposedMethod

Basic Idea

DoA Kernels

Time-difference ofArrival(TDoA)

Superpositionof DoA Kernels

CNMF Modelfor SCMObservations

CNMF ModelAlgo

ReconstructionandClustering

Direction ofWeightsClustering

Reference

Introduction literature Survey

What can matrix represent

What can matrix represent

System of equations

User rating matrix

ImageMatrix structure in graph theory

Adjacent matrixDistance matrix

Badri, Gokul and Phani DOA based SCM for BSS April 10, 2016 8 / 29

Direction ofArrival Based

SpatialCovarianceModel For

Blind SourceSeparation[1]

BadriPatro,GokulKrishnan &

Phani Reddy

Introduction

ProblemStatement

literatureSurvey

Matrixfactorization

Back GroundWork

Source MixingModels

SignalRepresentation

ConvolutiveMixing Model inSpatialCovarianceDomain

ProposedMethod

Basic Idea

DoA Kernels

Time-difference ofArrival(TDoA)

Superpositionof DoA Kernels

CNMF Modelfor SCMObservations

CNMF ModelAlgo

ReconstructionandClustering

Direction ofWeightsClustering

Reference

Introduction literature Survey

What can matrix represent

What can matrix represent

System of equations

User rating matrix

ImageMatrix structure in graph theory

Adjacent matrixDistance matrix

Badri, Gokul and Phani DOA based SCM for BSS April 10, 2016 8 / 29

Direction ofArrival Based

SpatialCovarianceModel For

Blind SourceSeparation[1]

BadriPatro,GokulKrishnan &

Phani Reddy

Introduction

ProblemStatement

literatureSurvey

Matrixfactorization

Back GroundWork

Source MixingModels

SignalRepresentation

ConvolutiveMixing Model inSpatialCovarianceDomain

ProposedMethod

Basic Idea

DoA Kernels

Time-difference ofArrival(TDoA)

Superpositionof DoA Kernels

CNMF Modelfor SCMObservations

CNMF ModelAlgo

ReconstructionandClustering

Direction ofWeightsClustering

Reference

Introduction literature Survey

What can matrix represent

What can matrix represent

System of equations

User rating matrix

ImageMatrix structure in graph theory

Adjacent matrixDistance matrix

Badri, Gokul and Phani DOA based SCM for BSS April 10, 2016 8 / 29

Direction ofArrival Based

SpatialCovarianceModel For

Blind SourceSeparation[1]

BadriPatro,GokulKrishnan &

Phani Reddy

Introduction

ProblemStatement

literatureSurvey

Matrixfactorization

Back GroundWork

Source MixingModels

SignalRepresentation

ConvolutiveMixing Model inSpatialCovarianceDomain

ProposedMethod

Basic Idea

DoA Kernels

Time-difference ofArrival(TDoA)

Superpositionof DoA Kernels

CNMF Modelfor SCMObservations

CNMF ModelAlgo

ReconstructionandClustering

Direction ofWeightsClustering

Reference

Introduction literature Survey

matrix factorization methods

Matrix factorization methods

LU decomposition

Solving system of equations

Singular Value Decomposition(SVD)Low rank matrix approximationPseudo-inverse

Probabilistic Matrix Factorization(PMF)Recommendation system

Non-negative Matrix Factorization(NMF)Learning the parts of objects

Badri, Gokul and Phani DOA based SCM for BSS April 10, 2016 9 / 29

Direction ofArrival Based

SpatialCovarianceModel For

Blind SourceSeparation[1]

BadriPatro,GokulKrishnan &

Phani Reddy

Introduction

ProblemStatement

literatureSurvey

Matrixfactorization

Back GroundWork

Source MixingModels

SignalRepresentation

ConvolutiveMixing Model inSpatialCovarianceDomain

ProposedMethod

Basic Idea

DoA Kernels

Time-difference ofArrival(TDoA)

Superpositionof DoA Kernels

CNMF Modelfor SCMObservations

CNMF ModelAlgo

ReconstructionandClustering

Direction ofWeightsClustering

Reference

Introduction literature Survey

matrix factorization methods

Matrix factorization methods

LU decomposition

Solving system of equations

Singular Value Decomposition(SVD)Low rank matrix approximationPseudo-inverse

Probabilistic Matrix Factorization(PMF)Recommendation system

Non-negative Matrix Factorization(NMF)Learning the parts of objects

Badri, Gokul and Phani DOA based SCM for BSS April 10, 2016 9 / 29

Direction ofArrival Based

SpatialCovarianceModel For

Blind SourceSeparation[1]

BadriPatro,GokulKrishnan &

Phani Reddy

Introduction

ProblemStatement

literatureSurvey

Matrixfactorization

Back GroundWork

Source MixingModels

SignalRepresentation

ConvolutiveMixing Model inSpatialCovarianceDomain

ProposedMethod

Basic Idea

DoA Kernels

Time-difference ofArrival(TDoA)

Superpositionof DoA Kernels

CNMF Modelfor SCMObservations

CNMF ModelAlgo

ReconstructionandClustering

Direction ofWeightsClustering

Reference

Introduction literature Survey

matrix factorization methods

Matrix factorization methods

LU decomposition

Solving system of equations

Singular Value Decomposition(SVD)Low rank matrix approximationPseudo-inverse

Probabilistic Matrix Factorization(PMF)Recommendation system

Non-negative Matrix Factorization(NMF)Learning the parts of objects

Badri, Gokul and Phani DOA based SCM for BSS April 10, 2016 9 / 29

Direction ofArrival Based

SpatialCovarianceModel For

Blind SourceSeparation[1]

BadriPatro,GokulKrishnan &

Phani Reddy

Introduction

ProblemStatement

literatureSurvey

Matrixfactorization

Back GroundWork

Source MixingModels

SignalRepresentation

ConvolutiveMixing Model inSpatialCovarianceDomain

ProposedMethod

Basic Idea

DoA Kernels

Time-difference ofArrival(TDoA)

Superpositionof DoA Kernels

CNMF Modelfor SCMObservations

CNMF ModelAlgo

ReconstructionandClustering

Direction ofWeightsClustering

Reference

Introduction literature Survey

matrix factorization methods

Matrix factorization methods

LU decomposition

Solving system of equations

Singular Value Decomposition(SVD)Low rank matrix approximationPseudo-inverse

Probabilistic Matrix Factorization(PMF)Recommendation system

Non-negative Matrix Factorization(NMF)Learning the parts of objects

Badri, Gokul and Phani DOA based SCM for BSS April 10, 2016 9 / 29

Direction ofArrival Based

SpatialCovarianceModel For

Blind SourceSeparation[1]

BadriPatro,GokulKrishnan &

Phani Reddy

Introduction

ProblemStatement

literatureSurvey

Matrixfactorization

Back GroundWork

Source MixingModels

SignalRepresentation

ConvolutiveMixing Model inSpatialCovarianceDomain

ProposedMethod

Basic Idea

DoA Kernels

Time-difference ofArrival(TDoA)

Superpositionof DoA Kernels

CNMF Modelfor SCMObservations

CNMF ModelAlgo

ReconstructionandClustering

Direction ofWeightsClustering

Reference

Introduction literature Survey

matrix factorization methods

Matrix factorization methods

LU decomposition

Solving system of equations

Singular Value Decomposition(SVD)Low rank matrix approximationPseudo-inverse

Probabilistic Matrix Factorization(PMF)Recommendation system

Non-negative Matrix Factorization(NMF)Learning the parts of objects

Badri, Gokul and Phani DOA based SCM for BSS April 10, 2016 9 / 29

Direction ofArrival Based

SpatialCovarianceModel For

Blind SourceSeparation[1]

BadriPatro,GokulKrishnan &

Phani Reddy

Introduction

ProblemStatement

literatureSurvey

Matrixfactorization

Back GroundWork

Source MixingModels

SignalRepresentation

ConvolutiveMixing Model inSpatialCovarianceDomain

ProposedMethod

Basic Idea

DoA Kernels

Time-difference ofArrival(TDoA)

Superpositionof DoA Kernels

CNMF Modelfor SCMObservations

CNMF ModelAlgo

ReconstructionandClustering

Direction ofWeightsClustering

Reference

Introduction literature Survey

matrix factorization methods

Matrix factorization methods

LU decomposition

Solving system of equations

Singular Value Decomposition(SVD)Low rank matrix approximationPseudo-inverse

Probabilistic Matrix Factorization(PMF)Recommendation system

Non-negative Matrix Factorization(NMF)Learning the parts of objects

Badri, Gokul and Phani DOA based SCM for BSS April 10, 2016 9 / 29

Direction ofArrival Based

SpatialCovarianceModel For

Blind SourceSeparation[1]

BadriPatro,GokulKrishnan &

Phani Reddy

Introduction

ProblemStatement

literatureSurvey

Matrixfactorization

Back GroundWork

Source MixingModels

SignalRepresentation

ConvolutiveMixing Model inSpatialCovarianceDomain

ProposedMethod

Basic Idea

DoA Kernels

Time-difference ofArrival(TDoA)

Superpositionof DoA Kernels

CNMF Modelfor SCMObservations

CNMF ModelAlgo

ReconstructionandClustering

Direction ofWeightsClustering

Reference

Introduction literature Survey

matrix factorization methods

Matrix factorization methods

LU decomposition

Solving system of equations

Singular Value Decomposition(SVD)Low rank matrix approximationPseudo-inverse

Probabilistic Matrix Factorization(PMF)Recommendation system

Non-negative Matrix Factorization(NMF)Learning the parts of objects

Badri, Gokul and Phani DOA based SCM for BSS April 10, 2016 9 / 29

Direction ofArrival Based

SpatialCovarianceModel For

Blind SourceSeparation[1]

BadriPatro,GokulKrishnan &

Phani Reddy

Introduction

ProblemStatement

literatureSurvey

Matrixfactorization

Back GroundWork

Source MixingModels

SignalRepresentation

ConvolutiveMixing Model inSpatialCovarianceDomain

ProposedMethod

Basic Idea

DoA Kernels

Time-difference ofArrival(TDoA)

Superpositionof DoA Kernels

CNMF Modelfor SCMObservations

CNMF ModelAlgo

ReconstructionandClustering

Direction ofWeightsClustering

Reference

Introduction literature Survey

matrix factorization methods

Matrix factorization methods

LU decomposition

Solving system of equations

Singular Value Decomposition(SVD)Low rank matrix approximationPseudo-inverse

Probabilistic Matrix Factorization(PMF)Recommendation system

Non-negative Matrix Factorization(NMF)Learning the parts of objects

Badri, Gokul and Phani DOA based SCM for BSS April 10, 2016 9 / 29

Direction ofArrival Based

SpatialCovarianceModel For

Blind SourceSeparation[1]

BadriPatro,GokulKrishnan &

Phani Reddy

Introduction

ProblemStatement

literatureSurvey

Matrixfactorization

Back GroundWork

Source MixingModels

SignalRepresentation

ConvolutiveMixing Model inSpatialCovarianceDomain

ProposedMethod

Basic Idea

DoA Kernels

Time-difference ofArrival(TDoA)

Superpositionof DoA Kernels

CNMF Modelfor SCMObservations

CNMF ModelAlgo

ReconstructionandClustering

Direction ofWeightsClustering

Reference

Introduction literature Survey

matrix factorization methods

Matrix factorization methods

LU decomposition

Solving system of equations

Singular Value Decomposition(SVD)Low rank matrix approximationPseudo-inverse

Probabilistic Matrix Factorization(PMF)Recommendation system

Non-negative Matrix Factorization(NMF)Learning the parts of objects

Badri, Gokul and Phani DOA based SCM for BSS April 10, 2016 9 / 29

Direction ofArrival Based

SpatialCovarianceModel For

Blind SourceSeparation[1]

BadriPatro,GokulKrishnan &

Phani Reddy

Introduction

ProblemStatement

literatureSurvey

Matrixfactorization

Back GroundWork

Source MixingModels

SignalRepresentation

ConvolutiveMixing Model inSpatialCovarianceDomain

ProposedMethod

Basic Idea

DoA Kernels

Time-difference ofArrival(TDoA)

Superpositionof DoA Kernels

CNMF Modelfor SCMObservations

CNMF ModelAlgo

ReconstructionandClustering

Direction ofWeightsClustering

Reference

Introduction literature Survey

NMF (Paatero and Tapper, 1994)

Badri, Gokul and Phani DOA based SCM for BSS April 10, 2016 10 / 29

Direction ofArrival Based

SpatialCovarianceModel For

Blind SourceSeparation[1]

BadriPatro,GokulKrishnan &

Phani Reddy

Introduction

ProblemStatement

literatureSurvey

Matrixfactorization

Back GroundWork

Source MixingModels

SignalRepresentation

ConvolutiveMixing Model inSpatialCovarianceDomain

ProposedMethod

Basic Idea

DoA Kernels

Time-difference ofArrival(TDoA)

Superpositionof DoA Kernels

CNMF Modelfor SCMObservations

CNMF ModelAlgo

ReconstructionandClustering

Direction ofWeightsClustering

Reference

Introduction literature Survey

NMF (@Author)*1

1Credit Goes to AuthorBadri, Gokul and Phani DOA based SCM for BSS April 10, 2016 11 / 29

Direction ofArrival Based

SpatialCovarianceModel For

Blind SourceSeparation[1]

BadriPatro,GokulKrishnan &

Phani Reddy

Introduction

ProblemStatement

literatureSurvey

Matrixfactorization

Back GroundWork

Source MixingModels

SignalRepresentation

ConvolutiveMixing Model inSpatialCovarianceDomain

ProposedMethod

Basic Idea

DoA Kernels

Time-difference ofArrival(TDoA)

Superpositionof DoA Kernels

CNMF Modelfor SCMObservations

CNMF ModelAlgo

ReconstructionandClustering

Direction ofWeightsClustering

Reference

Introduction literature Survey

NMF (@Author)*1

1Credit Goes to AuthorBadri, Gokul and Phani DOA based SCM for BSS April 10, 2016 12 / 29

Direction ofArrival Based

SpatialCovarianceModel For

Blind SourceSeparation[1]

BadriPatro,GokulKrishnan &

Phani Reddy

Introduction

ProblemStatement

literatureSurvey

Matrixfactorization

Back GroundWork

Source MixingModels

SignalRepresentation

ConvolutiveMixing Model inSpatialCovarianceDomain

ProposedMethod

Basic Idea

DoA Kernels

Time-difference ofArrival(TDoA)

Superpositionof DoA Kernels

CNMF Modelfor SCMObservations

CNMF ModelAlgo

ReconstructionandClustering

Direction ofWeightsClustering

Reference

Introduction literature Survey

NMF (Paatero and Tapper, 1994)

Badri, Gokul and Phani DOA based SCM for BSS April 10, 2016 13 / 29

Direction ofArrival Based

SpatialCovarianceModel For

Blind SourceSeparation[1]

BadriPatro,GokulKrishnan &

Phani Reddy

Introduction

ProblemStatement

literatureSurvey

Matrixfactorization

Back GroundWork

Source MixingModels

SignalRepresentation

ConvolutiveMixing Model inSpatialCovarianceDomain

ProposedMethod

Basic Idea

DoA Kernels

Time-difference ofArrival(TDoA)

Superpositionof DoA Kernels

CNMF Modelfor SCMObservations

CNMF ModelAlgo

ReconstructionandClustering

Direction ofWeightsClustering

Reference

Introduction literature Survey

NMF ([12,14,15,16,17,20])*1

NMF have been proposed for separation of soundsources both with single and multichannel mixtures.

In the NMF separation framework the spatialproperties of the sources can be modeled using aspatial covariance matrix (SCM) for each source ateach STFT frequency bin [18][22].

Such extensions are hereafter referred to ascomplex-valued NMF (CNMF).

SCM denotes the mixing of the sources by magnitudeand phase differences between the recorded channels,and is not dependent on the absolute phase of thesource signal.

1Credit Goes to AuthorBadri, Gokul and Phani DOA based SCM for BSS April 10, 2016 14 / 29

Direction ofArrival Based

SpatialCovarianceModel For

Blind SourceSeparation[1]

BadriPatro,GokulKrishnan &

Phani Reddy

Introduction

ProblemStatement

literatureSurvey

Matrixfactorization

Back GroundWork

Source MixingModels

SignalRepresentation

ConvolutiveMixing Model inSpatialCovarianceDomain

ProposedMethod

Basic Idea

DoA Kernels

Time-difference ofArrival(TDoA)

Superpositionof DoA Kernels

CNMF Modelfor SCMObservations

CNMF ModelAlgo

ReconstructionandClustering

Direction ofWeightsClustering

Reference

Introduction literature Survey

NMF ([12,14,15,16,17,20])*1

NMF have been proposed for separation of soundsources both with single and multichannel mixtures.

In the NMF separation framework the spatialproperties of the sources can be modeled using aspatial covariance matrix (SCM) for each source ateach STFT frequency bin [18][22].

Such extensions are hereafter referred to ascomplex-valued NMF (CNMF).

SCM denotes the mixing of the sources by magnitudeand phase differences between the recorded channels,and is not dependent on the absolute phase of thesource signal.

1Credit Goes to AuthorBadri, Gokul and Phani DOA based SCM for BSS April 10, 2016 14 / 29

Direction ofArrival Based

SpatialCovarianceModel For

Blind SourceSeparation[1]

BadriPatro,GokulKrishnan &

Phani Reddy

Introduction

ProblemStatement

literatureSurvey

Matrixfactorization

Back GroundWork

Source MixingModels

SignalRepresentation

ConvolutiveMixing Model inSpatialCovarianceDomain

ProposedMethod

Basic Idea

DoA Kernels

Time-difference ofArrival(TDoA)

Superpositionof DoA Kernels

CNMF Modelfor SCMObservations

CNMF ModelAlgo

ReconstructionandClustering

Direction ofWeightsClustering

Reference

Introduction literature Survey

NMF ([12,14,15,16,17,20])*1

NMF have been proposed for separation of soundsources both with single and multichannel mixtures.

In the NMF separation framework the spatialproperties of the sources can be modeled using aspatial covariance matrix (SCM) for each source ateach STFT frequency bin [18][22].

Such extensions are hereafter referred to ascomplex-valued NMF (CNMF).

SCM denotes the mixing of the sources by magnitudeand phase differences between the recorded channels,and is not dependent on the absolute phase of thesource signal.

1Credit Goes to AuthorBadri, Gokul and Phani DOA based SCM for BSS April 10, 2016 14 / 29

Direction ofArrival Based

SpatialCovarianceModel For

Blind SourceSeparation[1]

BadriPatro,GokulKrishnan &

Phani Reddy

Introduction

ProblemStatement

literatureSurvey

Matrixfactorization

Back GroundWork

Source MixingModels

SignalRepresentation

ConvolutiveMixing Model inSpatialCovarianceDomain

ProposedMethod

Basic Idea

DoA Kernels

Time-difference ofArrival(TDoA)

Superpositionof DoA Kernels

CNMF Modelfor SCMObservations

CNMF ModelAlgo

ReconstructionandClustering

Direction ofWeightsClustering

Reference

Introduction literature Survey

NMF ([12,14,15,16,17,20])*1

NMF have been proposed for separation of soundsources both with single and multichannel mixtures.

In the NMF separation framework the spatialproperties of the sources can be modeled using aspatial covariance matrix (SCM) for each source ateach STFT frequency bin [18][22].

Such extensions are hereafter referred to ascomplex-valued NMF (CNMF).

SCM denotes the mixing of the sources by magnitudeand phase differences between the recorded channels,and is not dependent on the absolute phase of thesource signal.

1Credit Goes to AuthorBadri, Gokul and Phani DOA based SCM for BSS April 10, 2016 14 / 29

Direction ofArrival Based

SpatialCovarianceModel For

Blind SourceSeparation[1]

BadriPatro,GokulKrishnan &

Phani Reddy

Introduction

ProblemStatement

literatureSurvey

Matrixfactorization

Back GroundWork

Source MixingModels

SignalRepresentation

ConvolutiveMixing Model inSpatialCovarianceDomain

ProposedMethod

Basic Idea

DoA Kernels

Time-difference ofArrival(TDoA)

Superpositionof DoA Kernels

CNMF Modelfor SCMObservations

CNMF ModelAlgo

ReconstructionandClustering

Direction ofWeightsClustering

Reference

Back Ground Work Source Mixing Models

Source Mixing Models

Array capture consists of a mixture of sound sourcesconvolved with their spatial responses.

xm (t) =K∑

k=1

∑τ

hmk (τ) sk (t − τ)

Which can be approximated as,

Xil ≈K∑

k=1

hiksik =K∑

k=1

yilk

where ,xil of the capture Xil = [Xil1, . . . .,XilM ]

Badri, Gokul and Phani DOA based SCM for BSS April 10, 2016 15 / 29

Direction ofArrival Based

SpatialCovarianceModel For

Blind SourceSeparation[1]

BadriPatro,GokulKrishnan &

Phani Reddy

Introduction

ProblemStatement

literatureSurvey

Matrixfactorization

Back GroundWork

Source MixingModels

SignalRepresentation

ConvolutiveMixing Model inSpatialCovarianceDomain

ProposedMethod

Basic Idea

DoA Kernels

Time-difference ofArrival(TDoA)

Superpositionof DoA Kernels

CNMF Modelfor SCMObservations

CNMF ModelAlgo

ReconstructionandClustering

Direction ofWeightsClustering

Reference

Back Ground Work Source Mixing Models

Source Mixing Models

Array capture consists of a mixture of sound sourcesconvolved with their spatial responses.

xm (t) =K∑

k=1

∑τ

hmk (τ) sk (t − τ)

Which can be approximated as,

Xil ≈K∑

k=1

hiksik =K∑

k=1

yilk

where ,xil of the capture Xil = [Xil1, . . . .,XilM ]

Badri, Gokul and Phani DOA based SCM for BSS April 10, 2016 15 / 29

Direction ofArrival Based

SpatialCovarianceModel For

Blind SourceSeparation[1]

BadriPatro,GokulKrishnan &

Phani Reddy

Introduction

ProblemStatement

literatureSurvey

Matrixfactorization

Back GroundWork

Source MixingModels

SignalRepresentation

ConvolutiveMixing Model inSpatialCovarianceDomain

ProposedMethod

Basic Idea

DoA Kernels

Time-difference ofArrival(TDoA)

Superpositionof DoA Kernels

CNMF Modelfor SCMObservations

CNMF ModelAlgo

ReconstructionandClustering

Direction ofWeightsClustering

Reference

Back Ground Work Source Mixing Models

Source Mixing Models

Array capture consists of a mixture of sound sourcesconvolved with their spatial responses.

xm (t) =K∑

k=1

∑τ

hmk (τ) sk (t − τ)

Which can be approximated as,

Xil ≈K∑

k=1

hiksik =K∑

k=1

yilk

where ,xil of the capture Xil = [Xil1, . . . .,XilM ]

Badri, Gokul and Phani DOA based SCM for BSS April 10, 2016 15 / 29

Direction ofArrival Based

SpatialCovarianceModel For

Blind SourceSeparation[1]

BadriPatro,GokulKrishnan &

Phani Reddy

Introduction

ProblemStatement

literatureSurvey

Matrixfactorization

Back GroundWork

Source MixingModels

SignalRepresentation

ConvolutiveMixing Model inSpatialCovarianceDomain

ProposedMethod

Basic Idea

DoA Kernels

Time-difference ofArrival(TDoA)

Superpositionof DoA Kernels

CNMF Modelfor SCMObservations

CNMF ModelAlgo

ReconstructionandClustering

Direction ofWeightsClustering

Reference

Back Ground Work Signal Representation

Badri, Gokul and Phani DOA based SCM for BSS April 10, 2016 16 / 29

Direction ofArrival Based

SpatialCovarianceModel For

Blind SourceSeparation[1]

BadriPatro,GokulKrishnan &

Phani Reddy

Introduction

ProblemStatement

literatureSurvey

Matrixfactorization

Back GroundWork

Source MixingModels

SignalRepresentation

ConvolutiveMixing Model inSpatialCovarianceDomain

ProposedMethod

Basic Idea

DoA Kernels

Time-difference ofArrival(TDoA)

Superpositionof DoA Kernels

CNMF Modelfor SCMObservations

CNMF ModelAlgo

ReconstructionandClustering

Direction ofWeightsClustering

Reference

Back Ground Work Signal Representation

numbered lists

SCM calculated at each time-frequency point.

Magntiude-square root version of array capture.

Abs phase of signal transformed to phase differencebetween microphone pair

Badri, Gokul and Phani DOA based SCM for BSS April 10, 2016 16 / 29

Direction ofArrival Based

SpatialCovarianceModel For

Blind SourceSeparation[1]

BadriPatro,GokulKrishnan &

Phani Reddy

Introduction

ProblemStatement

literatureSurvey

Matrixfactorization

Back GroundWork

Source MixingModels

SignalRepresentation

ConvolutiveMixing Model inSpatialCovarianceDomain

ProposedMethod

Basic Idea

DoA Kernels

Time-difference ofArrival(TDoA)

Superpositionof DoA Kernels

CNMF Modelfor SCMObservations

CNMF ModelAlgo

ReconstructionandClustering

Direction ofWeightsClustering

Reference

Back Ground Work Signal Representation

numbered lists

SCM calculated at each time-frequency point.

Magntiude-square root version of array capture.

Abs phase of signal transformed to phase differencebetween microphone pair

Badri, Gokul and Phani DOA based SCM for BSS April 10, 2016 16 / 29

Direction ofArrival Based

SpatialCovarianceModel For

Blind SourceSeparation[1]

BadriPatro,GokulKrishnan &

Phani Reddy

Introduction

ProblemStatement

literatureSurvey

Matrixfactorization

Back GroundWork

Source MixingModels

SignalRepresentation

ConvolutiveMixing Model inSpatialCovarianceDomain

ProposedMethod

Basic Idea

DoA Kernels

Time-difference ofArrival(TDoA)

Superpositionof DoA Kernels

CNMF Modelfor SCMObservations

CNMF ModelAlgo

ReconstructionandClustering

Direction ofWeightsClustering

Reference

Back Ground Work Signal Representation

numbered lists

SCM calculated at each time-frequency point.

Magntiude-square root version of array capture.

Abs phase of signal transformed to phase differencebetween microphone pair

Badri, Gokul and Phani DOA based SCM for BSS April 10, 2016 16 / 29

Direction ofArrival Based

SpatialCovarianceModel For

Blind SourceSeparation[1]

BadriPatro,GokulKrishnan &

Phani Reddy

Introduction

ProblemStatement

literatureSurvey

Matrixfactorization

Back GroundWork

Source MixingModels

SignalRepresentation

ConvolutiveMixing Model inSpatialCovarianceDomain

ProposedMethod

Basic Idea

DoA Kernels

Time-difference ofArrival(TDoA)

Superpositionof DoA Kernels

CNMF Modelfor SCMObservations

CNMF ModelAlgo

ReconstructionandClustering

Direction ofWeightsClustering

Reference

Back Ground Work Convolutive Mixing Model in Spatial Covariance Domain

numbered lists with single pauses

1 Mixing in Spatial Domain.

2 defined by, replacing each term by its covariancecounter-part .

Badri, Gokul and Phani DOA based SCM for BSS April 10, 2016 17 / 29

Direction ofArrival Based

SpatialCovarianceModel For

Blind SourceSeparation[1]

BadriPatro,GokulKrishnan &

Phani Reddy

Introduction

ProblemStatement

literatureSurvey

Matrixfactorization

Back GroundWork

Source MixingModels

SignalRepresentation

ConvolutiveMixing Model inSpatialCovarianceDomain

ProposedMethod

Basic Idea

DoA Kernels

Time-difference ofArrival(TDoA)

Superpositionof DoA Kernels

CNMF Modelfor SCMObservations

CNMF ModelAlgo

ReconstructionandClustering

Direction ofWeightsClustering

Reference

Proposed Method Basic Idea

Basic Idea

Basic Idea:

BSS via estimation of source SCM of STFT of mixturesignal.

SCM model is combined with a parameter estimationis formulated in a complex-valued non-negative matrixfactorization (CNMF) framework

Badri, Gokul and Phani DOA based SCM for BSS April 10, 2016 18 / 29

Direction ofArrival Based

SpatialCovarianceModel For

Blind SourceSeparation[1]

BadriPatro,GokulKrishnan &

Phani Reddy

Introduction

ProblemStatement

literatureSurvey

Matrixfactorization

Back GroundWork

Source MixingModels

SignalRepresentation

ConvolutiveMixing Model inSpatialCovarianceDomain

ProposedMethod

Basic Idea

DoA Kernels

Time-difference ofArrival(TDoA)

Superpositionof DoA Kernels

CNMF Modelfor SCMObservations

CNMF ModelAlgo

ReconstructionandClustering

Direction ofWeightsClustering

Reference

Proposed Method Basic Idea

Basic Idea

Block diagram of Proposed Algorithm:

Badri, Gokul and Phani DOA based SCM for BSS April 10, 2016 19 / 29

Direction ofArrival Based

SpatialCovarianceModel For

Blind SourceSeparation[1]

BadriPatro,GokulKrishnan &

Phani Reddy

Introduction

ProblemStatement

literatureSurvey

Matrixfactorization

Back GroundWork

Source MixingModels

SignalRepresentation

ConvolutiveMixing Model inSpatialCovarianceDomain

ProposedMethod

Basic Idea

DoA Kernels

Time-difference ofArrival(TDoA)

Superpositionof DoA Kernels

CNMF Modelfor SCMObservations

CNMF ModelAlgo

ReconstructionandClustering

Direction ofWeightsClustering

Reference

Proposed Method DoA Kernels

Time-difference of Arrival:

Time-difference of Arrival:

Badri, Gokul and Phani DOA based SCM for BSS April 10, 2016 20 / 29

Direction ofArrival Based

SpatialCovarianceModel For

Blind SourceSeparation[1]

BadriPatro,GokulKrishnan &

Phani Reddy

Introduction

ProblemStatement

literatureSurvey

Matrixfactorization

Back GroundWork

Source MixingModels

SignalRepresentation

ConvolutiveMixing Model inSpatialCovarianceDomain

ProposedMethod

Basic Idea

DoA Kernels

Time-difference ofArrival(TDoA)

Superpositionof DoA Kernels

CNMF Modelfor SCMObservations

CNMF ModelAlgo

ReconstructionandClustering

Direction ofWeightsClustering

Reference

Proposed Method DoA Kernels

Time-difference of Arrival:

Time-difference of Arrival:

Figure: Array geometry consisting of two microphones m and n asseen from above, source azimuth angle given as θ.

Badri, Gokul and Phani DOA based SCM for BSS April 10, 2016 21 / 29

Direction ofArrival Based

SpatialCovarianceModel For

Blind SourceSeparation[1]

BadriPatro,GokulKrishnan &

Phani Reddy

Introduction

ProblemStatement

literatureSurvey

Matrixfactorization

Back GroundWork

Source MixingModels

SignalRepresentation

ConvolutiveMixing Model inSpatialCovarianceDomain

ProposedMethod

Basic Idea

DoA Kernels

Time-difference ofArrival(TDoA)

Superpositionof DoA Kernels

CNMF Modelfor SCMObservations

CNMF ModelAlgo

ReconstructionandClustering

Direction ofWeightsClustering

Reference

Proposed Method DoA Kernels

Superposition of DoA Kernels:

DoA kernels for each look direction O and at eachfrequency I is denoted by Wio

source spatial image S = H ∗ S

Badri, Gokul and Phani DOA based SCM for BSS April 10, 2016 22 / 29

Direction ofArrival Based

SpatialCovarianceModel For

Blind SourceSeparation[1]

BadriPatro,GokulKrishnan &

Phani Reddy

Introduction

ProblemStatement

literatureSurvey

Matrixfactorization

Back GroundWork

Source MixingModels

SignalRepresentation

ConvolutiveMixing Model inSpatialCovarianceDomain

ProposedMethod

Basic Idea

DoA Kernels

Time-difference ofArrival(TDoA)

Superpositionof DoA Kernels

CNMF Modelfor SCMObservations

CNMF ModelAlgo

ReconstructionandClustering

Direction ofWeightsClustering

Reference

Proposed Method CNMF Model for SCM Observations

CNMF Model for SCM Observations

CNMF Model for SCM Observations:

Badri, Gokul and Phani DOA based SCM for BSS April 10, 2016 23 / 29

Direction ofArrival Based

SpatialCovarianceModel For

Blind SourceSeparation[1]

BadriPatro,GokulKrishnan &

Phani Reddy

Introduction

ProblemStatement

literatureSurvey

Matrixfactorization

Back GroundWork

Source MixingModels

SignalRepresentation

ConvolutiveMixing Model inSpatialCovarianceDomain

ProposedMethod

Basic Idea

DoA Kernels

Time-difference ofArrival(TDoA)

Superpositionof DoA Kernels

CNMF Modelfor SCMObservations

CNMF ModelAlgo

ReconstructionandClustering

Direction ofWeightsClustering

Reference

Proposed Method CNMF Model Algo

CNMF Cost Function:

CNMF Cost Function:

Badri, Gokul and Phani DOA based SCM for BSS April 10, 2016 24 / 29

Direction ofArrival Based

SpatialCovarianceModel For

Blind SourceSeparation[1]

BadriPatro,GokulKrishnan &

Phani Reddy

Introduction

ProblemStatement

literatureSurvey

Matrixfactorization

Back GroundWork

Source MixingModels

SignalRepresentation

ConvolutiveMixing Model inSpatialCovarianceDomain

ProposedMethod

Basic Idea

DoA Kernels

Time-difference ofArrival(TDoA)

Superpositionof DoA Kernels

CNMF Modelfor SCMObservations

CNMF ModelAlgo

ReconstructionandClustering

Direction ofWeightsClustering

Reference

Proposed Method CNMF Model Algo

Algorithm Updates for the Non-negativeParameters:

Algorithm Updates for the Non-negative Parameters:

Badri, Gokul and Phani DOA based SCM for BSS April 10, 2016 25 / 29

Direction ofArrival Based

SpatialCovarianceModel For

Blind SourceSeparation[1]

BadriPatro,GokulKrishnan &

Phani Reddy

Introduction

ProblemStatement

literatureSurvey

Matrixfactorization

Back GroundWork

Source MixingModels

SignalRepresentation

ConvolutiveMixing Model inSpatialCovarianceDomain

ProposedMethod

Basic Idea

DoA Kernels

Time-difference ofArrival(TDoA)

Superpositionof DoA Kernels

CNMF Modelfor SCMObservations

CNMF ModelAlgo

ReconstructionandClustering

Direction ofWeightsClustering

Reference

Proposed Method CNMF Model Algo

Algorithm Updates for the SCM Model Parameters

Algorithm Updates for the SCM Model Parameters:

Badri, Gokul and Phani DOA based SCM for BSS April 10, 2016 26 / 29

Direction ofArrival Based

SpatialCovarianceModel For

Blind SourceSeparation[1]

BadriPatro,GokulKrishnan &

Phani Reddy

Introduction

ProblemStatement

literatureSurvey

Matrixfactorization

Back GroundWork

Source MixingModels

SignalRepresentation

ConvolutiveMixing Model inSpatialCovarianceDomain

ProposedMethod

Basic Idea

DoA Kernels

Time-difference ofArrival(TDoA)

Superpositionof DoA Kernels

CNMF Modelfor SCMObservations

CNMF ModelAlgo

ReconstructionandClustering

Direction ofWeightsClustering

Reference

Proposed Method CNMF Model Algo

Algorithm Implementation:

Algorithm Implementation:

Badri, Gokul and Phani DOA based SCM for BSS April 10, 2016 27 / 29

Direction ofArrival Based

SpatialCovarianceModel For

Blind SourceSeparation[1]

BadriPatro,GokulKrishnan &

Phani Reddy

Introduction

ProblemStatement

literatureSurvey

Matrixfactorization

Back GroundWork

Source MixingModels

SignalRepresentation

ConvolutiveMixing Model inSpatialCovarianceDomain

ProposedMethod

Basic Idea

DoA Kernels

Time-difference ofArrival(TDoA)

Superpositionof DoA Kernels

CNMF Modelfor SCMObservations

CNMF ModelAlgo

ReconstructionandClustering

Direction ofWeightsClustering

Reference

Reconstruction and Clustering Direction of Weights Clustering

K mean:

K mean:

Apply k-means clustering on the spatial weights zko ,

No of cluster is equal to the number of sound sources

Badri, Gokul and Phani DOA based SCM for BSS April 10, 2016 28 / 29

Direction ofArrival Based

SpatialCovarianceModel For

Blind SourceSeparation[1]

BadriPatro,GokulKrishnan &

Phani Reddy

Introduction

ProblemStatement

literatureSurvey

Matrixfactorization

Back GroundWork

Source MixingModels

SignalRepresentation

ConvolutiveMixing Model inSpatialCovarianceDomain

ProposedMethod

Basic Idea

DoA Kernels

Time-difference ofArrival(TDoA)

Superpositionof DoA Kernels

CNMF Modelfor SCMObservations

CNMF ModelAlgo

ReconstructionandClustering

Direction ofWeightsClustering

Reference

Reconstruction and Clustering Direction of Weights Clustering

K mean:

K mean:

Apply k-means clustering on the spatial weights zko ,

No of cluster is equal to the number of sound sources

Badri, Gokul and Phani DOA based SCM for BSS April 10, 2016 28 / 29

Direction ofArrival Based

SpatialCovarianceModel For

Blind SourceSeparation[1]

BadriPatro,GokulKrishnan &

Phani Reddy

Introduction

ProblemStatement

literatureSurvey

Matrixfactorization

Back GroundWork

Source MixingModels

SignalRepresentation

ConvolutiveMixing Model inSpatialCovarianceDomain

ProposedMethod

Basic Idea

DoA Kernels

Time-difference ofArrival(TDoA)

Superpositionof DoA Kernels

CNMF Modelfor SCMObservations

CNMF ModelAlgo

ReconstructionandClustering

Direction ofWeightsClustering

Reference

Reconstruction and Clustering Direction of Weights Clustering

Source Reconstruction:

Source Reconstruction:

Badri, Gokul and Phani DOA based SCM for BSS April 10, 2016 29 / 29

Direction ofArrival Based

SpatialCovarianceModel For

Blind SourceSeparation[1]

BadriPatro,GokulKrishnan &

Phani Reddy

Introduction

ProblemStatement

literatureSurvey

Matrixfactorization

Back GroundWork

Source MixingModels

SignalRepresentation

ConvolutiveMixing Model inSpatialCovarianceDomain

ProposedMethod

Basic Idea

DoA Kernels

Time-difference ofArrival(TDoA)

Superpositionof DoA Kernels

CNMF Modelfor SCMObservations

CNMF ModelAlgo

ReconstructionandClustering

Direction ofWeightsClustering

Reference

Reference

[1] J. Nikunen., ‘‘Direction of Arrival Based Spatial Covariance Mode forBlind Sound Source Separation”,IEEE/ACM trans.., vol. 22, no. 3, p.727, 2014.

[2] A. Ozerov. and C. Fevotte.,‘‘Multichannel nonnegativematrixfactorization in convolutive mixtures for audio source separation”,IEEETrans. Audio, Speech, Lang. Process., vol. 18, no. 3, pp. 550563, Mar.2010.

[3] H. Sawada, H. Kameoka, S. Araki, and N. Ueda,, ‘‘New formulationsand efficient algorithms for multichannel nmf,”,in Proc. IEEE WorkshopApplicat. Signal Process. Audio Acoust. (WASPAA),pp. 153156, 2011.

[4] H. Sawada, H. Kameoka, S. Araki, and N. Ueda,‘‘Multichannelextensions of non-negative matrix factorization with complex-valueddata.”,IEEE Trans. Audio, Speech, Lang. Process., vol. 21, no. 5, pp.971982, May 2013.

[5] H Sawada, R Mukai, S Araki, S Makino,‘‘A robust and precise methodfor solving the permutation problem of frequency-domain blind sourceseparation”,Speech and Audio Processing, IEEE Transactions on, 2004.

Badri, Gokul and Phani DOA based SCM for BSS April 10, 2016 29 / 29