We study the problem of dictionary learning for signals that can berepresented as polynomials or polynomial matrices, such as convolutive signalswith time delays or acoustic impulse responses. Recently, we developed a methodfor polynomial dictionary learning based on the fact that a polynomial matrixcan be expressed as a polynomial with matrix coefficients, where thecoefficient of the polynomial at each time lag is a scalar matrix. However, apolynomial matrix can be also equally represented as a matrix with polynomialelements. In this paper, we develop an alternative method for learning apolynomial dictionary and a sparse representation method for polynomial signalreconstruction based on this model. The proposed methods can be used directlyto operate on the polynomial matrix without having to access its coefficientsmatrices. We demonstrate the performance of the proposed method for acousticimpulse response modeling.
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