Time-efficient filtering of imaging polarimetric data by checking physical realizability of experimental Mueller matrices

Motivation Imaging Mueller polarimetry has already proved its potential for biomedicine, remote sensing, and metrology. The real-time applications of this modality require both video rate image acquisition and fast data post-processing algorithms. First, one must check the physical realizability of the experimental Mueller matrices in order to filter out non-physical data, i.e. to test the positive semi-definiteness of the 4 x 4 Hermitian coherency matrix calculated from the elements of corresponding Mueller matrix pixel-wise. For this purpose, we compared the execution time for the calculations of (i) eigenvalues, (ii) Cholesky decomposition, (iii) Sylvester's criterion, and (iv) coefficients of the characteristic polynomial (two different approaches) of the Hermitian coherency matrix, all calculated for the experimental Mueller matrix images (600 pixels x 700 pixels) of mouse uterine cervix. The calculations were performed using C++ and Julia programming languages.Results Our results showed the superiority of the algorithm (iv) based on the simplification via Pauli matrices over other algorithms for our dataset. The sequential implementation of latter algorithm on a single core already satisfies the requirements of real-time polarimetric imaging. This can be further amplified by the proposed parallelization (e.g. we achieve a 5-fold speed up on six cores).Availability and implementation The source codes of the algorithms and experimental data are available at https://github.com/pogudingleb/mueller_matrices.