Blind Audio Source Separation - Overcomplete Dictionaries
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].
6) Overcomplete Dictionaries
6.1) Short-Time Discrete Cosine Transform
The STDCT with 50% overlap was used and the results for the various
sets of signals are shown here.
Reconstructed Speech Signal 1
Reconstructed Speech Signal 2
Reconstructed Speech Signal 3
Reconstructed Musical Signal 1
Reconstructed Musical Signal 2
Reconstructed Musical Signal 3
Reconstructed Percussion Signal 1
Reconstructed Percussion Signal 2
Reconstructed Percussion Signal 3
Reconstructed Speech Signal 1
Reconstructed Musical Signal 2
Reconstructed Percussion Signal 3
6.2) Hybrid Transforms
Reconstructed Speech Signal 1
Reconstructed Speech Signal 2
Reconstructed Speech Signal 3
Reconstructed Musical Signal 1
Reconstructed Musical Signal 2
Reconstructed Musical Signal 3
Reconstructed Percussion Signal 1
Reconstructed Percussion Signal 2
Reconstructed Percussion Signal 3
Reconstructed Speech Signal 1
Reconstructed Musical Signal 2
Reconstructed Percussion Signal 3
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