Nonnegative low rank tensor approximations with multidimensional image applications

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.