A Bayesian approach for polarimetric data reduction: the Mueller imaging case

Abstract

In this paper, we extend to the Mueller imaging framework a formerly introduced Bayesian approach dealing with polarimetric data reduction and robust clustering of polarization encoded images in the piecewise constant case. The extension was made possible thanks to a suitable writing of the observation model in the Mueller context that relies on the system's coherency matrix and Cholesky decomposition such that the admissibility constraints are easily captured. This generalization comes at the cost of nonlinearity with respect to the parameters that have to be estimated. This estimation-clustering problem is tackled in a Bayesian framework where a hierarchical stochastic model based on a Markov random field proposed by Potts is used. This fully unsupervised approach is extensively tested over synthetic data as well as real Mueller images.

Mueller matrix interpolation in polarization optics

“…The coherency matrix C is related to H by: (4) In fact, as demonstrated by Aiello et al [15], there are infinitely many Hermitian matrices generated by M which differ from H by an unitary transformation. Each of these Hermitian matrices is related to the coefficients of the decomposition of matrix F on a specific basis of  .…”

“…noticing that many experimental coherency matrices of media exhibited in the literature are positive definite matrices (their four eigenvalues are strictly positive).Under this hypothesis, the set of coherency matrices may be restricted to HPD (4), the manifold of Hermitian Positive Definite matrices of dimension 4. It is clear that we don't take into account the Mueller matrices corresponding to a singular coherency matrix.…”

“…Following the definition of the LE distance, the geodesic curve or interpolation curve between H 1 and H 2 , two elements of HPD (4), is given by:…”

“…The measurement of the Mueller matrix entries attached to each pixel in an image is named Mueller imaging. The development of optical devices and systems [1], calibration procedures [2] and measurement inversion methods [3] [4] produced Mueller imaging systems with low noise measurement where the physical constraints on Mueller matrices are taken into account. These works contributed to popularize this imaging approach and examples of Mueller matrix imaging can be found for characterizing biological objects [5] or scattering media [6], with applications in dermatology [7], ophthalmology [8] or physics [9][10] for instance.…”

Joint filtering estimation of Stokes vector images based on a nonlocal means approach

“…The Bayesian framework yields neat solutions to the polarimetric data reduction problem for the case of piecewise constant signatures [3,4]. The case of smoothly varying signatures has also been addressed, for example by Valenzuela and Fessler [5] and by Sfikas et al [6].…”