Acoustically Inspired Probabilistic Time-domain Music Transcription and Source Separation.

PhD ThesisAutomatic music transcription (AMT) and source separation are important computational tasks, which can help to understand, analyse and process music recordings. The main purpose of AMT is to estimate, from an observed audio recording, a latent symbolic representation of a piece of music (piano-roll). In this sense, in AMT the duration and location of every note played is reconstructed from a mixture recording. The related task of source separation aims to estimate the latent functions or source signals that were mixed together in an audio recording. This task requires not only the duration and location of every event present in the mixture, but also the reconstruction of the waveform of all the individual sounds. Most methods for AMT and source separation rely on the magnitude of time-frequency representations of the analysed recording, i.e., spectrograms, and often arbitrarily discard phase information. On one hand, this decreases the time resolution in AMT. On the other hand, discarding phase information corrupts the reconstruction in source separation, because the phase of each source-spectrogram must be approximated. There is thus a need for models that circumvent phase approximation, while operating at sample-rate resolution. This thesis intends to solve AMT and source separation together from an unified perspective. For this purpose, Bayesian non-parametric signal processing, covariance kernels designed for audio, and scalable variational inference are integrated to form efficient and acoustically-inspired probabilistic models. To circumvent phase approximation while keeping sample-rate resolution, AMT and source separation are addressed from a Bayesian time-domain viewpoint. That is, the posterior distribution over the waveform of each sound event in the mixture is computed directly from the observed data. For this purpose, Gaussian processes (GPs) are used to define priors over the sources/pitches. GPs are probability distributions over functions, and its kernel or covariance determines the properties of the functions sampled from a GP. Finally, the GP priors and the available data (mixture recording) are combined using Bayes' theorem in order to compute the posterior distributions over the sources/pitches. Although the proposed paradigm is elegant, it introduces two main challenges. First, as mentioned before, the kernel of the GP priors determines the properties of each source/pitch function, that is, its smoothness, stationariness, and more importantly its spectrum. Consequently, the proposed model requires the design of flexible kernels, able to learn the rich frequency content and intricate properties of audio sources. To this end, spectral mixture (SM) kernels are studied, and the Mat ern spectral mixture (MSM) kernel is introduced, i.e. a modified version of the SM covariance function. The MSM kernel introduces less strong smoothness, thus it is more suitable for modelling physical processes. Second, the computational complexity of GP inference scales cubically with the number of audio samples. Therefore, the application of GP models to large audio signals becomes intractable. To overcome this limitation, variational inference is used to make the proposed model scalable and suitable for signals in the order of hundreds of thousands of data points. The integration of GP priors, kernels intended for audio, and variational inference could enable AMT and source separation time-domain methods to reconstruct sources and transcribe music in an efficient and informed manner. In addition, AMT and source separation are current challenges, because the spectra of the sources/pitches overlap with each other in intricate ways. Thus, the development of probabilistic models capable of differentiating sources/pitches in the time domain, despite the high similarity between their spectra, opens the possibility to take a step towards solving source separation and automatic music transcription. We demonstrate the utility of our methods using real and synthesized music audio datasets for various types of musical instruments

Compilación de Proyectos de Investigación desde el año 2003 al 2012

Listado de Proyectos de investigación de UPIICSA desde 2003 a 201