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

TL;DR

This paper introduces NLRT, a new algorithm for nonnegative low rank tensor approximation tailored for multi-dimensional images, outperforming existing nonnegative tensor factorization methods.

Contribution

The paper develops a novel alternating projections algorithm for nonnegative low Tucker rank tensor approximation, with proven convergence and improved performance.

Findings

NLRT outperforms state-of-the-art NTF methods on synthetic and real data.

The convergence of the manifold projection method is theoretically established.

Experimental results demonstrate superior approximation quality.

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.