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Linear Program Differentiation For Single-CHannel Speech Separation

Pearlmutter, Barak A. and Olsson, Rasmus K. (2005) Linear Program Differentiation For Single-CHannel Speech Separation. International Journal of Imaging Systems and Technology, 15. pp. 18-33.

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Abstract

Many apparently difficult problems can be solved by reduction to linear programming. Such problems are often subproblems within larger systems. When gradient optimisation of the entire larger system is desired, it is necessary to propagate gradients through the internally-invoked LP solver. For instance, when an intermediate quantity z is the solution to a linear program involving constraint matrix A, a vector of sensitivities dE/dz will induce sensitivities dE/dA. Here we show how these can be efficiently calculated, when they exist. This allows algorithmic differentiation to be applied to algorithms that invoke linear programming solvers as subroutines, as is common when using sparse representations in signal processing. Here we apply it to gradient optimisation of overcomplete dictionaries for maximally sparse representations of a speech corpus. The dictionaries are employed in a single-channel speech separation task, leading to 5 dB and 8 dB target-to-interference ratio improvements for same-gender and opposite-gender mixtures, respectively. Furthermore, the dictionaries are successfully applied to a speaker identification task.

Item Type: Article
Keywords: Sparse methods, source separation
Subjects: Science & Engineering > Computer Science
Item ID: 565
Depositing User: Dr. Barak Pearlmutter
Date Deposited: 15 Jun 2007
Journal or Publication Title: International Journal of Imaging Systems and Technology
Publisher: Wiley
Refereed: Yes
URI:

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