A Polynomial Dictionary Learning Method for Acoustic Impulse Response Modeling

Dictionary design is an important issue in sparse representations. As compared with pre-defined dictionaries, dictionaries learned from training signals may provide a better fit to the signals of interest. Existing dictionary learning algorithms have focussed overwhelmingly on standard matrix (i.e. with scalar elements), and little attention has been paid to polynomial matrix, despite its widespread use for describing con-volutive signals and for modelling acoustic channels in both room and underwater acoustics. In this paper, we present a method for polynomial matrix based dictionary learning by extending the widely used K-SVD algorithm to the polynomial matrix case. The atoms in the learned dictionary form the basic building components for the impulse responses. Through the control of the sparsity in the coding stage, the proposed method can be used for denoising of acoustic impulse responses, as demonstrated by simulations for both noiseless and noisy data.