Implementation of a Denoising Algorithm Based on High-Order Singular Value Decomposition of Tensors
Fabien Feschet
published
2019-06-13
reference
Fabien Feschet, Implementation of a Denoising Algorithm Based on High-Order Singular Value Decomposition of Tensors, Image Processing On Line, 9 (2019), pp. 158–182. https://doi.org/10.5201/ipol.2019.226

Communicated by Pablo Arias
Demo edited by Pablo Arias

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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