Blind Audio Source Separation - Conclusion
We deal with the case where the sources are linearly mixed and the
mixtures are underdetermined. Hence, A has more columns than rows.
Sparsity of the sources is vital for good separation. Bayesian methods
such as the Gibbs Sampler (a standard MCMC simulation method) are used
to estimate the sources and the mixing matrix in the presence of noise.
I.I.D. Gaussian noise was added to the observations, which resulted in
an SNR of about 16 dB. The mixing matrix used is given by A = [0.4000
0.8315 0.5657; -0.6928 -0.3444 0.5657].
7) Conclusion
In this project, we have investigated the use of different bases and
overcomplete dictionaries
in Blind Audio Source Separation. A Bayesian approach based on Gibbs
Sampling was used to estimate the sources in the transform domain, the
mixing matrix A and the noise standard deviation sigma. Various
transforms were applied on different sets of signals and they yielded
vastly diverse results. Sparsity of the sources was a central theme
of the whole project and was found to be integral to the source
separation algorithm’s performance.
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