Abstract
This chapter shows how sparse solutions can be obtained for a range of problems in a Bayesian setting by using prior models on sparsity structure. As an example, a model to remove impulse and background noise from audio signals via their representation in time-frequency space using Gabor wavelets is presented. A number of prior models for the sparse structure of the signal in this space are introduced, including simple Bernoulli priors on each coefficient, Markov chains linking neighbouring coefficients in time or frequency, and Markov random fields, imposing two dimensional coherence on the coefficients. The effect of each of these priors on the reconstruction of a corrupted audio signal is shown. Impulse removal is also covered, with similar sparsity priors being applied to the location of impulse noise in the audio signal. Inference is performed by sampling from the posterior distribution of the model variables using a Gibbs sampler.
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Murphy, J., Godsill, S. (2014). Structured Sparse Bayesian Modelling for Audio Restoration. In: Carmi, A., Mihaylova, L., Godsill, S. (eds) Compressed Sensing & Sparse Filtering. Signals and Communication Technology. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38398-4_14
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DOI: https://doi.org/10.1007/978-3-642-38398-4_14
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