The translation of imaging Mueller polarimetry to clinical practice is often hindered by large footprint and relatively slow acquisition speed of the existing instruments. Using polarization-sensitive camera as a detector may reduce instrument dimensions and allow data streaming at video rate. However, only the first three rows of a complete ${4}\times {4}$ Mueller matrix can be measured. To overcome this hurdle we developed a machine learning approach using sequential neural network algorithm for the reconstruction of missing elements of a Mueller matrix from the measured elements of the first three rows. The algorithm was trained and tested on the dataset of polarimetric images of various excised human tissues (uterine cervix, colon, skin, brain) acquired with two different imaging Mueller polarimeters operating in either reflection (wide-field imaging system) or transmission (microscope) configurations at different wavelengths of 550 nm and 385 nm, respectively. Reconstruction performance was evaluated using various error metrics, all of which confirmed low error values. The reconstruction of full images of the fourth row of Mueller matrix with GPU parallelization and increasing batch size took less than 50 milliseconds. It suggests that a machine learning approach with parallel processing of all image pixels combined with the partial Mueller polarimeter operating at video rate can effectively substitute for the complete Mueller polarimeter and produce accurate maps of depolarization, linear retardance and orientation of the optical axis of biological tissues, which can be used for medical diagnosis in clinical settings.

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, ie to test the positive semi-definiteness of the 4 × 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 × 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 6 cores). AVAILABILITY AND IMPLEMENTATION: The source codes of the algorithms and experimental data are available at https://github.com/pogudingleb/mueller_matrices.