Implementation of a Denoising Algorithm based on High-Order Singular Value Decomposition of Tensors
Fabien Feschet
⚠ This is a preprint. It may change before it is accepted for publication.

Abstract

This article presents an implementation of a denoising algorithm based on High-Order Singular Value Decomposition (HOSVD) of tensors. It belongs to the class of patch-based methods such as BM3D and NL-Bayes. It exploits the grouping of similar patches in a local neighbourhood into a 3D matrix also called a third order tensor. Instead of performing different processing in different dimension, as in BM3D for instance, it is based on the decomposition of a tensor simultaneously in all dimensions reducing it to a core tensor in a similar way as SVD does for matrices in computing the diagonal matrix of singular values. The core tensor is filtered and a tensor is reconstructed by inverting the HOSVD. As common in patch-based algorithms, all tensors containing a pixel are then merged to produce an output image.

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