Robust tensor regression with applications in imaging

Abstract

Tensor regression models have gained popularity in problems where covariates are tensors (multidimensional arrays) such as images. Tensor regression models are able to efficiently exploit the temporal and/or spatial structure of tensor covariates (e.g., in hyperspectral or fMRI images) by imposing a low-rank assumption on the parameter tensor. In this paper, we propose a robust tensor regression estimation method within the framework of Kruskal tensor regression model. We consider Huber's concomitant criterion for regression and scale as it offers a good tradeoff between robustness and computational feasibility. An efficient alternating minimization algorithm is proposed for estimating the unknown regression parameters. Our simulation studies with synthetic image signals illustrate that the proposed estimator performs similarly compared to benchmark method when errors are Gaussians but offers superior performance in heavy-tailed noise, while having similar computational complexity.