Fourier Priors for Audio Restoration

Traditional frequency-based audio restoration methods require complete data in order to perform a deterministic Fourier transform before handling the data in the frequency domain. We investigate the use of a probabilistic Fourier transform method, suggested by Storkey [27], in an audio restoration application, focussing on inferring missing and clipped points from music data. A practical implementation of the probabilistic Fourier transform method is necessary; we explore a number of optimisers and their associated performance and problems. We then investigate suitable models for Fourier priors for audio–in particular, music–data, and compare the performance of the proba-bilistic Fourier transform technique with Gaussian and t-distributed Fourier priors. We find that t-distribution priors are better suited to audio data than Gaussian, but in gen-eral it is difficult to perform effective audio restoration with incorporating perceptual information to the model. i noises