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.

Speech Signals. Click here to go to the speech page.

Reconstructed Speech Signal 1
Reconstructed Speech Signal 2
Reconstructed Speech Signal 3

Musical Signals. Click here to go to the music page.

Reconstructed Musical Signal 1
Reconstructed Musical Signal 2
Reconstructed Musical Signal 3

Percussion Signals. Click here to go to the percussion page.

Reconstructed Percussion Signal 1
Reconstructed Percussion Signal 2
Reconstructed Percussion Signal 3

Combination of Signals. Click here to go to the combination of signals page.

Reconstructed Speech Signal 1
Reconstructed Musical Signal 2
Reconstructed Percussion Signal 3

6.2) Hybrid Transforms

Speech Signals. Click here to go to the speech page.

Reconstructed Speech Signal 1
Reconstructed Speech Signal 2
Reconstructed Speech Signal 3

Musical Signals. Click here to go to the music page.

Reconstructed Musical Signal 1
Reconstructed Musical Signal 2
Reconstructed Musical Signal 3

Percussion Signals. Click here to go to the percussion page.

Reconstructed Percussion Signal 1
Reconstructed Percussion Signal 2
Reconstructed Percussion Signal 3

Combination of Signals. Click here to go to the combination of signals page.

Reconstructed Speech Signal 1
Reconstructed Musical Signal 2
Reconstructed Percussion Signal 3



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