Matrix of Polynomials Model based Polynomial Dictionary Learning Methodudfor Acoustic Impulse Response Modeling

摘要

We study the problem of dictionary learning for signals thatudcan be represented as polynomials or polynomial matrices, suchudas convolutive signals with time delays or acoustic impulse responses.udRecently, we developed a method for polynomial dictionaryudlearning based on the fact that a polynomial matrix canudbe expressed as a polynomial with matrix coefficients, whereudthe coefficient of the polynomial at each time lag is a scalar matrix.udHowever, a polynomial matrix can be also equally representedudas a matrix with polynomial elements. In this paper, weuddevelop an alternative method for learning a polynomial dictionaryudand a sparse representation method for polynomial signaludreconstruction based on this model. The proposed methods canudbe used directly to operate on the polynomial matrix withoutudhaving to access its coefficients matrices. We demonstrate theudperformance of the proposed method for acoustic impulse responseudmodeling.