Signal subspace methods for speech enhancement

This thesis focus on the theory analysis and algorithm aspects of signal subspace methods used for speech enhancement in digital speech processing The problem is approached by initially performing an analysis of subspace principles applied to speech signals in order to characterize the usefulness of de ning a signal subspace for this application The theory is formulated by means of the singular value decomposition or the eigendecomposition and subspace methods are linked to ltering in the frequency domain Nonparametric speech enhancement using linear signal subspace based estimation of the clean signal from the noisy signal is reviewed and connections between existing algorithms and litterature are explored An analysis of the practical behavior of the estimators is given and aspects regarding their performance in the case with prewhitening is covered The relation to the popular spectral subtraction approach is discussed and the origin of the musical noise is pointed out A possible way to reduce the latter is devised In the noisy case model based estimation is a nonlinear problem which is normally solved by iterative techniques However a new idea based on multi microphone inverse ltering is presented where the solution is obtained by subspace methods The algorithm aspects of signal subspace methods are discussed in terms of the rank revealing ULV ULLV decompositions which are numerically stable and can be cheaply updated when a new data sample is present The potential of the decompositions when applied to speech problems are analyzed and di erent estimation strategies are suggested Again the practical behavior of the estimators are analyzed A recursive ULLV algorithm for a so called sliding window estimation is presented which is new in its complete treatment and implementation Many aspects of the algorithm are discussed in details and important considerations are pointed out Both the ULV ULLV algorithms and the subspace based enhancement algorithms are implemented in a Matlab toolbox Throughout the thesis the speech enhancement application illustrates the power and ro bustness of the subspace approach and a number of illustrative examples are given Peter S K Hansen iii

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