Sparse and Supervised Tucker Decomposition for Tensor-based Multichannel Noise Reduction

Recently, tensor-based multichannel noise reduction has been widely studied by many researchers. In this framework, researchers represent observed multichannel signals as a 3-dimensional tensor. Then, the tensor's multi-linear filtering theory is adopted to reduce spatially white or colored noise. The alternating least square approach is adopted and these algorithms generally need several iterations to converge. In this paper, we use the tensor decomposition theory and develop a supervised machine learning algorithm to obtain adaptive factoring matrices. The obtained matrices can transform the input noisy tensor into a sparse core tensor. Then, we reduce the noise by manipulating coefficients in the core tensor according to their amplitude. Specifically, we start from the minimum risk point of view and calculate an optimal threshold that kills the small entries and keep only the large entries in the core tensor. Our simulations show the proposed algorithm can significantly reduce spatially white noise and cause little distortion.