Physically-Constrained Block-Term Tensor Decomposition for Polarimetric Image Recovery

Abstract

This paper introduces a complete approach for the recovery of polarimetric images from experimental intensity measurements. In many applications, such images collect, at each pixel, a Stokes vector encoding the polarization state of light. By representing a Stokes vector image as a third-order tensor, we propose a new physicallyconstrained block-term tensor decomposition called Stokes-BTD. The proposed model is flexible and comes with broad identifiability guarantees. Moreover, physical constraints ensure meaningful interpretation of low-rank terms as Stokes vectors. In practice, Stokes images must be recovered from indirect, intensity measurements. To this aim, we implement two recovery algorithms for Stokes-BTD based on constrained alternated optimization and highlight constraints related to Stokes vectors. Numerical experiments on synthetic and real data illustrate the potential of the approach.