Bayesian Modelling of Music: Algorithmic Advances and Experimental Studies of Shift-Invariant Sparse Coding
Year: 2006
Type: dissertation
Abstract: In order to perform many signal processing tasks such as classification, \npattern recognition and coding, it is helpful to specify a signal model in \nterms of meaningful signal structures. In general, designing such a model \nis complicated and for many signals it is not feasible to specify the appropriate \nstructure. Adaptive models overcome this problem by learning \nstructures from a set of signals. Such adaptive models need to be general \nenough, so that they can represent relevant structures. However, more \ngeneral models often require additional constraints to guide the learning \nprocedure. \n \nIn this thesis a sparse coding model is used to model time-series. Relevant \nfeatures can often occur at arbitrary locations and the model has to be \nable to reflect this uncertainty, which is achieved using a shift-invariant \nsparse coding formulation. In order to learn model parameters, we use \nBayesian statistical methods, however, analytic solutions to this learning \nproblem are not available and approximations have to be introduced. In \nthis thesis we study three approximations, one based on an analytical \nintegral approximation and two based on Monte Carlo approximations. \nBut even with these approximations, a solution to the learning problem \nis computationally too expensive for the applications under investigation. \nTherefore, we introduce further approximations by subset selection. \n \nMusic signals are highly structured time-series and offer an ideal testbed \nfor the studied model. We show the emergence of note- and score-like features \nfrom a polyphonic piano recording and compare the results to those \nobtained with a different model suggested in the literature. Furthermore, \nwe show that the model finds structures that can be assigned to an individual \nsource in a mixture. This is shown with an example of a mixture \ncontaining guitar and vocal parts for which blind source separation can \nbe performed based on the shift-invariant sparse coding model.
Author: Thomas Blumensath
Language: English
Topic: Music and Audio Processing
Subfield: Signal Processing
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2151985930