Main flattening directions and Quadtree decomposition for multi-way Wiener filtering

Abstract

Previous studies have shown that multi-way Wiener filtering improves the restoration of tensors impaired by an additive white Gaussian noise. Multi-way Wiener filtering is based on the distinction between noise and signal subspaces. In this paper, we show that the lower is the signal subspace dimension, the better is the restored tensor. To reduce the signal subspace dimension, we propose a method based on array processing technique to estimate main orientations in a flattened tensor. The rotation of a tensor of its main orientation values permits to concentrate the information along either rows or columns of the flattened tensor. We show that multi-way Wiener filtering performed on the rotated noisy tensor enables an improved recovery of signal tensor. Moreover, we propose in this paper a quadtree decomposition to avoid a blurry effect in the recovered tensor by multi-way Wiener filtering. We show that this proposed block processing reduces the whole blur and restores local characteristics of the signal tensor. Thus, we show that multi-way Wiener filtering is significantly improved thanks to rotations of the estimated main orientations of tensors and a block processing approach.