Nonnegative Low Rank Tensor Approximation and its Application to Multi-dimensional Images
This provides an improved method for multi-dimensional image processing, though it is incremental as it builds on existing nonnegative tensor factorization approaches.
The paper tackles the problem of approximating nonnegative tensors from multi-dimensional imaging by developing a nonnegative low Tucker rank tensor approximation algorithm, demonstrating that it outperforms state-of-the-art nonnegative tensor factorization methods in experiments.
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.