Thomas Blumensath

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Research Group : Centre for Digital Music

Research Project: Shift-Invariant Sparse Coding

Current Research

Environmental sounds, speech and music are a highly structured acoustic signals. In my work I try to find novel ways of discovering these structures from raw audio data. This work is inspired by the amazing capability of the processing that occur in the human brain, which is highly adapted to extract structures from sensory signals to build internal representations of objects in the world. It is often assumed that the mammalian brain achieves this task by finding representations with reduced redundancy in comparison to the primary sensory signal. This can be achieved by building representations of independent features. This independence constraint is a direct implication of the normally used definition of an object. What we normally label as an individual object is often a set of components, which are strongly dependent. Different objects differ by their independencies. This is also true for acoustic objects such as individual notes in a musical performance.

My work involves trying to find representations of individual objects by using mathematical models to find the dependencies and independencies of acoustic components. This can be accomplished by searching for efficient and independent representations of audio signals. This task is best dealt with in a statistical framework, which is the natural description of dependencies in an uncertain environment. I therefore use Bayesian methods for unsupervised machine learning. These methods adapt a generative model, which is specified by prior and conditional distributions, to fit the training data.

This approach can find signal descriptions which differ from the traditional signal processing representations such as the ones obtained by standard time-frequency analysis methods. Most traditional transforms do not find independent representations as they rely on the use of a fixed dictionary of basis functions and a linear analysis stage. To overcome this restriction, statistical methods can be used, which are able to extract the basis function from the source signal itself in order to find independent representations. This is often achieved by Principle Component Analysis (PCA), Independent Component Analysis (ICA) and more recently by Sparse Coding. All of these methods, however, work on a fixed time grid, correlating the basis functions with the signal at fixed time locations. Recent time-frequency decompositions have been proposed, which work with overcomplete basis functions and which can include functions at arbitrary positions. These methods fit basis functions to the best possible time location.

In order to find independent and efficient representations of time-series such as audio signals, the representation has to be invariant to shifts. My research therefor is aimed at developing algorithms that are able to extract basis functions from an audio signal, which are independent from their time position in the original signal. As most natural audio signals can be assumed to be a sparse composition of individual basis functions, this can be achieved by Sparse Coding with a shift-invariance constraint .

The applications for such a decomposition are very broad. Possible applications include: audio coding, music transcription, blind source separation, audio restoration and noise reduction. Furthermore, as the generative model formulation is very general, the application to other problems such as images and general time-series is feasible.

Further research interests

My research interests include: Mathematical Methods in Signal Processing, Statistical Models for Audio Analysis, Statistical Signal Processing, Higher Order Statistics, Sparse Decomposition, Unsupervised Learning in Statistical Models, Mathematical Principles of Human Perception, Neural Computation and generally everything I don't understand.

Publications

Mark D. Plumbley, Samer A. Abdallah, Thomas Blumensath and Mike Davies, "Sparse Representations of Polyphonic Music", To appear in EURASIP Signal Processing Journal.

Thomas Blumensath and Mike Davies, "Sparse and Shift-Invariant Representations of Music ". submitted for publication to IEEE transactions on Speech and Audio Processing.

Thomas Blumensath and Mike Davies, "Enforcing sparsity, shift-invariance and positivity in a Bayesian model of polyphonic music," in Proc. of the IEEE Workshop on Statistical Signal Processing (SSP05), July 2005

Thomas Blumensath and Mike Davies, "Unsupervised Learning of Sparse and Shift-Invariant Decompositions of Polyphonic Music", in Proc. Int. Conf. on Acoustics Speech and Signal Processing (ICASSP 2004), May 2004

Thomas Blumensath and Mike Davies, "On Shift-Invariant Sparse Coding ". In Proc. Int. Conf. on Independent Component Analysis (ICA 2004), Granada (Spain) , September 2004

Thomas Blumensath and Mike Davies, "A fast Importance Sampling Algorithm for Unsupervised Learning of Over-Complete Dictionaries", in Proc. Int. Conf. on Acoustics Speech and Signal Processing (ICASSP 2005), March 2005

Preprints/reprints available on request.