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A generalized multidimensional Wiener filter for denoising is adapted to hyperspectral images (HSIs). Multidimensional Wiener filtering (MWF) uses the signal subspace of each n-mode flattening matrix of the HSI, which is a third-order tensor. However, in the HSI case, the n-mode ranks are close to the n-mode dimensions. Thus, the signal subspace dimension can be underestimated. This leads to a loss of spatial resolution-edge blurring-and artifacts in the restored HSI. To cope with the underestimation while preserving edges, a new method is proposed. It estimates the relevant directions of flattening that may not be parallel to HSI dimensions. 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 decomposition to tensors in order to adapt the filtering to the local image characteristics. Comparative studies with MWF, principal component analysis-stationary wavelet transform, and channel-by-channel Wiener filtering show that our algorithm provides better performance while restoring impaired HYDICE HSIs.Index Terms-Flattening directions, hyperspectral, multidimensional Wiener filtering (MWF), quadtree, tensor.