Nonnegative low rank tensor approximations with multidimensional image applications

Tai Xiang Jiang, Michael K. Ng, Junjun Pan, Guang Jing Song*

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

15 Citations (Scopus)

Abstract

The main aim of this paper is to develop a new algorithm for computing a nonnegative low rank tensor approximation for nonnegative tensors that arise in many multidimensional imaging applications. Nonnegativity is one of the important properties, as each pixel value refers to a nonzero light intensity in image data acquisitions. Our approach is different from classical nonnegative tensor factorization (NTF), which requires each factorized matrix, and/or tensor, to be nonnegative. In this paper, we determine a nonnegative low Tucker rank tensor to approximate a given nonnegative tensor. We propose an alternating projections algorithm for computing such a nonnegative low rank tensor approximation, which is referred to as NLRT. The convergence of the proposed manifold projection method is established. The experimental results for synthetic data and multidimensional images are presented to demonstrate that the performance of NLRT is better than the state-of-the-art NTF methods.

Original languageEnglish
Pages (from-to)141-170
Number of pages30
JournalNumerische Mathematik
Volume153
Issue number1
Early online date29 Oct 2022
DOIs
Publication statusPublished - Jan 2023

Scopus Subject Areas

  • Computational Mathematics
  • Applied Mathematics

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