Nonnegative Low Rank Tensor Approximation and its Application to Multi-dimensional Images

2020/07/28 by Tai-Xiang Jiang, Jiang, Tai-Xiang, Michael K. Ng +5
Computer Science · Mathematics · Medicine · #Advanced Neuroimaging Techniques and Applications #Computer Vision and Pattern Recognition (cs.CV) #FOS: Computer and information sciences #FOS: Electrical engineering #FOS: Mathematics #Image and Signal Denoising Methods #Image and Video Processing (eess.IV) #Numerical Analysis (math.NA) #Tensor decomposition and applications #electronic engineering #information engineering

paper · pdf · doi:10.48550/arxiv.2007.14137

openalex publication_date 2020/07/28 · openalex created_date 2020/08/03 · openalex updated_date 2026/07/28

Abstract

The main aim of this paper is to develop a new algorithm for computing nonnegative low rank tensor approximation for nonnegative tensors that arise in many multi-dimensional imaging applications. Nonnegativity is one of the important property as each pixel value refers to nonzero light intensity in image data acquisition. 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 nonnegative low rank tensor approximation, which is referred to as NLRT. The convergence of the proposed manifold projection method is established. Experimental results for synthetic data and multi-dimensional images are presented to demonstrate the performance of NLRT is better than state-of-the-art NTF methods.

Citations

• Some Mathematical Notes on Three-Mode Factor Analysis
• Analysis of Individual Differences in Multidimensional Scaling Via an N-way Generalization of “Eckart-Young” Decomposition
• Tensor Decompositions and Applications
• Proximal Alternating Minimization and Projection Methods for Nonconvex Problems: An Approach Based on the Kurdyka-Łojasiewicz Inequality
• Tensor Decomposition for Signal Processing and Machine Learning

Related

• Nonnegative Low-Rank Tensor Completion via Dual Formulation with Applications to Image and Video Completion
• Analysis on Non-negative Factorizations and Applications
• Fast Tucker Rank Reduction for Non-Negative Tensors Using Mean-Field Approximation
• Tensor Completion via a Low-Rank Approximation Pursuit
• Nonnegative Low Rank Matrix Approximation for Nonnegative Matrices