Noise Removal From Hyperspectral Images by Multidimensional Filtering

A generalized multidimensional Wiener filter for denoising is adapted to hyperspectral images (HSIs). Commonly, multidimensional data filtering is based on data vectorization or matricization. Few new approaches have been proposed to deal with multidimensional data. Multidimensional Wiener filtering (MWF) is one of these techniques. It considers a multidimensional data set as a third-order tensor. It also relies on the separability between a signal subspace and a noise subspace. Using multilinear algebra, MWF needs to flatten the tensor. However, flattening is always orthogonally performed, which may not be adapted to data. In fact, as a Tucker-based filtering, MWF only considers the useful signal subspace. When the signal subspace and the noise subspace are very close, it is difficult to extract all the useful information. This may lead to artifacts and loss of spatial resolution in the restored HSI. Our proposed method estimates the relevant directions of tensor flattening that may not be parallel either to rows or columns. When rearranging data so that flattening can be performed in the estimated directions, the signal subspace dimension is reduced, and the signal-to-noise ratio is improved. We adapt the bidimensional straight-line detection algorithm that estimates the HSI main directions, which are used to flatten the HSI tensor. We also generalize the quadtree partitioning to tensors in order to adapt the filtering to the image discontinuities. Comparative studies with MWF, wavelet thresholding, and channel-by-channel Wiener filtering show that our algorithm provides better performance while restoring impaired HYDICE HSIs.     

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

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.