A new article is available in IPOL: http://www.ipol.im/pub/art/2019/226/
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
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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