Gamma Markov Random fields for audio source modelling

Audio processing tasks, such as source separation or denoising, require the construction of realistic models that reflect physical properties of audio signals. In this paper, we modelled the variances of time-frequency coefficients of audio signals with gamma Markov random fields (GMRFs) so that the dependencies between coefficients are captured. There is positive correlation between consecutive variance variables in this model and the strength of this correlation is determined by the coupling hyperparameters. Inference can be carried out using the Gibbs sampler or variational Bayes because the model is conditionally conjugate. However, the optimisation of the hyperparameters is not straightforward because of the intractable normalising constant. In this work, we used this model in denoising and single-channel source separation problems. The hyperparameters of the model are optimised using contrastive divergence and inference is performed using the Gibbs sampler.