Performance of Maximum Likelihood estimation of Mueller matrices taking into account physical realizability and Gaussian or Poisson noise statistics

We address constrained estimation of the Mueller matrices from noisy measurements, taking into account the physical realizability. Physical realizability is enforced based on the positive semi-definite Hermitian coherency matrix, and the statistics of the noise is taken into account by employing Maximum Likelihood (ML) method. We consider two types of noise sources frequently encountered in optical imaging systems: additive Gaussian noise and Poisson shot noise. In both cases, we demonstrate reduction of estimation error by enforcing the physical realizability constraint, and superiority of the ML constrained solutions compared to empirically constrained ones. The ML constrained estimation method proposed in this paper provides a justified and effective way to exploit experimental measurements of Mueller matrices.