  Imaging Mueller polarimetry has already proved its potential for metrology,
remote sensing and biomedicine. 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 4x4 Hermitian coherency matrix
calculated from the elements of the 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 of the Hermitian coherency matrix
using two different approaches, 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. Our
results showed the superiority of the algorithm iv), in particular, the version
based on the simplification via Pauli matrices, in terms of execution time for
our dataset, over other algorithms. The sequential implementation of the latter
algorithm on a single core already satisfies the requirements of real-time
polarimetric imaging in various domains. This can be further amplified by the
proposed parallelization (for example, we achieve a 5-fold speed up on 6
cores).
