Examples of Noise Reduction Using Multi-Gabor Dictionaries

Clean Signal

Noisy Signal (SNR 7 dB)

Bayesian single-resolution reconstruction (noise variance known)

Bayesian multi-resolution reconstruction (noise variance estimated)
Resolution level 0
Resolution level 1
Resolution level 2
Resolution level 3

Multi-gabor dictionary comparisons

Below is a short segment of speech, sampled at 16 kHz and artificially degraded by additive white Gaussian noise to yield a signal-to-noise ratio (SNR) of 20 dB. A reduced Gabor dictionary comprising four equi-spaced, overlapping resolutions levels, each of an approximate bandwidth of 3 kHz, was applied in order to estimate the underlying signal.

The figure below shows a comparison of the minimum mean-square error reconstruction of this signal, with the noise variance set to its true value, taken after the Markov chain of the employed Gibbs sampler appeared to have reached a stationary regime.

In this case the reduced dictionary performs on a par with the full dictionary. For this particular example, the resultant SNR for the reduced dictionary is only 1.5 dB lower than for the full one, and the required number of flops was reduced by a factor of 2.5. Additionally, the reduced dictionary yields a more parsimonious representation of the signal, employing approximately 7,000 atoms (out of a total of over 13,000) as compared to over 17,000 (out of a total of over 32,000) in the case of the full dictionary.

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