May 3 rd, 2010 Update

Outline Monday, May 3 rd 2  Audio spatialization  Performance evaluation (source separation)  Source separation  System overview  Demonstration (system)  Concentration measure and W-disjoint orthogonality  Adaptive time-frequency representation (TFR)  Demonstration (adaptive TFR)

Audio spatialization Monday, May 3 rd 3  Audio spatialization – a spatial rendering technique for conversion of the available audio into desired listening configuration  Analysis – separating individual sources  Re-synthesis – re-creating the desired listener-end configuration Available spatial audio (speakers) Analysis (source separation) separated sources Re-synthesis (convolving with HRIRs) Desired listener-end configuration (headphones)

Performance evaluation [1] Monday, May 3 rd 4 Estimated source and Original source Performance evaluation block Performance measures (ISR, SIR, SAR, SDR)  ISR = Image to Spatial-distortion Ratio  SIR = Source to Interference Ratio  SAR = Source to Artifacts Ratio  SDR = Source to Distortion Ratio

Performance evaluation Monday, May 3 rd 5  Estimated source image can be decomposed as  true source image,  error components  spatial distortion,  interference,  artifacts,

Performance evaluation Monday, May 3 rd 6

Source separation [2,3] Monday, May 3 rd 7 Mixtures (stereo) Time- frequency transform Source analysis Source synthesis Inverse time-frequency transform Separated sources (>=2)  Source separation – obtaining the estimates of the underlying sources, from a set of observations from the sensors  Time-frequency transform  Source analysis – estimation of mixing parameters  Source synthesis – estimation of sources  Inverse time-frequency representation

Mixing model Monday, May 3 rd 8  Anechoic mixing model  Mixtures, x i  Sources, s j  Under-determined (M < N)  M = Number of mixtures  N = Number of sources Figure: Anechoic mixing model – Audio is observed at the microphones with differing intensity and arrival times (because of propagation delays) but with no reverberations Source:P. O. Grady, B. Pearlmutter and S. Rickard, “Survey of sparse and non-sparse methods in source separation,” International Journal of Imaging Systems and Technology, 2005

Mixtures Monday, May 3 rd 9 Mixtures (stereo) Time-frequency transform Source analysis Source synthesis Inverse time-frequency transform Separated sources (>=2) Source 1 Source 2Source 3 Mixtures (stereo)

function – TFRStereo  Mixture (stereo)  Sampling frequency  DFT size  Window size  Hop size  Mixture TFRs InputsOutputs Monday, May 3 rd 10 Mixtures (stereo) Time-frequency transform Source analysis Source synthesis Inverse time-frequency transform Separated sources (>=2)

Time-frequency transform Monday, May 3 rd 11 Mixtures (stereo) Time-frequency transform Source analysis Source synthesis Inverse time-frequency transform Separated sources (>=2)

function – SourceAnalysis  Mixture TFRs  2-D histogram  Mixing parameters InputsOutputs Monday, May 3 rd 12 Mixtures (stereo) Time-frequency transform Source analysis Source synthesis Inverse time-frequency transform Separated sources (>=2)

Source analysis (estimation of mixing parameters) Monday, May 3 rd 13 Mixtures (stereo) Time-frequency transform Source analysis Source synthesis Inverse time-frequency transform Separated sources (>=2)

function – SourceSynthesis  Mixing parameters  Mixture TFRs  Estimation technique  DUET/LQBP  Estimated source masks  Estimated source TFRs InputsOutputs Monday, May 3 rd 14 Mixtures (stereo) Time-frequency transform Source analysis Source synthesis Inverse time-frequency transform Separated sources (>=2)

Source synthesis (estimation of sources) Monday, May 3 rd 15 Mixtures (stereo) Time-frequency transform Source analysis Source synthesis Inverse time-frequency transform Separated sources (>=2)

Monday, May 3 rd 16 Mixtures (stereo) Time-frequency transform Source analysis Source synthesis Inverse time-frequency transform Separated sources (>=2) Source synthesis (estimation of sources)

Monday, May 3 rd 17 Mixtures (stereo) Time-frequency transform Source analysis Source synthesis Inverse time-frequency transform Separated sources (>=2) Source synthesis (estimation of sources)

function – InverseTFR  Estimated source TFRs  Sampling frequency  Estimated sources InputsOutputs Monday, May 3 rd 18 Mixtures (stereo) Time-frequency transform Source analysis Source synthesis Inverse time-frequency transform Separated sources (>=2)

Inverse time-frequency transform Monday, May 3 rd 19 Mixtures (stereo) Time-frequency transform Source analysis Source synthesis Inverse time-frequency transform Separated sources (>=2) Orig. source 1 Orig. source 2 Orig. source 3 Source 1 Source 2 Source 3

Demonstration (system) Monday, May 3 rd 20 No. of sources (2)No. of sources (3) Mixture Original SAR SDR SIR ISR SAR SDR SIR ISR DFT size = 2048 Window size = 50 ms Hop size = 25 ms Sampling frequency = Hz all the values are in dB

Concentration measure Monday, May 3 rd 21  Requirement for source separation  W-disjoint orthogonality  Sparsity is an indicator of WDO [4]  Thus a sparser TFR is expected to satisfy WDO criterion to a greater extent  Commonly used sparsity measures [5]  Kurtosis  Gini Index

Monday, May 3 rd 22  Source separation demands (WDO)  Sparse time-frequency representation (TFR)  Some observations  Music/speech signals – different frequency components present at different time instants  Different analysis window lengths provide different sparsity [4]  Therefore, to obtain a sparser TFR  Use that analysis window length for a particular time-instant, which gives highest sparsity [6] Mixtures (stereo) Time-frequency transform Source analysis Source synthesis Inverse time-frequency transform Separated sources (>=2) Adaptive TFR

Monday, May 3 rd 23

Adaptive TFR Monday, May 3 rd 24

function – TFRStereo (modified)  Mixture (stereo)  Sampling frequency  DFT size  Window size  Window size default  Concentration measure  Mixture TFRs  Adapted window sequence InputsOutputs Monday, May 3 rd 25 Mixtures (stereo) Time-frequency transform Source analysis Source synthesis Inverse time-frequency transform Separated sources (>=2)

Monday, May 3 rd 26  Constraint  TFR should be invertible  Solution  Select analysis windows such that they satisfy constant over-lap add (COLA) criterion [7] Inverse adaptive TFR Mixtures (stereo) Time-frequency transform Source analysis Source synthesis Inverse time-frequency transform Separated sources (>=2)

Analysis windows (COLA) Monday, May 3 rd 27

function – InverseTFR (modified)  Estimated source TFRs  Sampling frequency  Adapted window sequence  Window size default  Estimated sources InputsOutputs Monday, May 3 rd 28 Mixtures (stereo) Time-frequency transform Source analysis Source synthesis Inverse time-frequency transform Separated sources (>=2)

Demonstration (adaptive TFR) Monday, May 3 rd 29 Source 1Source 2Source 3 Original ATFR (20:10:90 ms) SAR SDR SIR ISR TFR (60 ms) SAR SDR SIR ISR all the values are in dB

Demonstration (adaptive TFR) Monday, May 3 rd 30 Source 1Source 2Source 3 Original ATFR (20:10:90 ms) SAR SDR SIR ISR TFR (60 ms) SAR SDR SIR ISR all the values are in dB

References Monday, May 3 rd 31 1.E. Vincent, R. Gribonval and C. Fevotte, “Performance measurement in blind audio source separation,” IEEE Transactions on Audio, Speech and Language Processing, A. Jourjine, S. Rickard and O. Yilmaz, “Blind separation of disjoint orthogonal signals: demixing n sources from 2 mixtures,” IEEE Conference on Acoustics, Speech and Signal Processing, R. Saab, O. Yilmaz, M. J. Mckeown and R. Abugharbieh, “Underdetermined anechoic blind source separation via l q basis pursuit with q<1,” IEEE Transactions on Signal Processing, 2007

References Monday, May 3 rd 32 4.S. Rickard, “Sparse sources are separated sources,” European Signal Processing Conference, N. Hurley and S. Rickard, “Comparing measures of sparsity,” IEEE Transactions on Information Theory, D. L. Jones and T. Parks, “A high resolution data-adaptive time-frequency representation,” IEEE Transactions on Acoustics, Speech and Signal Processing, P. Basu, P. J. Wolfe, D. Rudoy, T. F. Quatieri and B. Dunn, “Adaptive short- time analysis-synthesis for speech enhancement,” IEEE Conference on Acoustics, Speech and Signal Processing, 2008

Questions ? Thank you