Matrix of Polynomials Model Based Polynomial Dictionary Learning Method for Acoustic Impulse Response Modeling.
2017
We study the problem of dictionary learning for signals that
can be represented as polynomials or polynomial matrices, such
as convolutive signals with time delays or acoustic impulse responses.
Recently, we developed a method for polynomial dictionary
learning based on the fact that a polynomial matrix can
be expressed as a polynomial with matrix coefficients, where
the coefficient of the polynomial at each time lag is a scalar matrix.
However, a polynomial matrix can be also equally represented
as a matrix with polynomial elements. In this paper, we
develop an alternative method for learning a polynomial dictionary
and a sparse representation method for polynomial signal
reconstruction based on this model. The proposed methods can
be used directly to operate on the polynomial matrix without
having to access its coefficients matrices. We demonstrate the
performance of the proposed method for acoustic impulse response
modeling.
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