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 physically-constrained 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 StokesBTD 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.