Implementation of a Denoising Algorithm Based on High-Order Singular Value Decomposition of Tensors

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 neighborhood into a 3D matrix also called a third order tensor. Instead of performing a different processing in each 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 it is common in patch-based algorithms, all tensors containing a pixel are then merged to produce an output image. Source Code The C++ source code, the code documentation, and the online demo are accessible at the IPOL web page of this article.(1) Compilation and usage instructions are included in the README.txt file of the archive.