Joint reconstruction of Stokes images from polarimetric measurements

Abstract

In the field of imaging polarimetry Stokes parameters are sought and must be inferred from noisy and blurred intensity measurements. Using a penalized-likelihood estimation framework we investigate reconstruction quality when estimating intensity images and then transforming to Stokes parameters, and when estimating Stokes parameters directly. We define our cost function for reconstruction by a weighted least-squares data fit term and a regularization penalty. We show that for quadratic regularization the estimators of Stokes and intensity images can be made equal by appropriate choice of regularization parameters. It is empirically shown that, when using edge preserving regularization, estimating the Stokes parameters directly leads to lower RMS error. Also, the addition of a cross channel regularization term further lowers the RMS error for both methods, especially in the case of low SNR.

On the performance of the physicality-constrained maximum-likelihood estimation of Stokes vector

“…If the intensity measurements are perturbed by noise, so is the estimated Stokes vector, and this noise may even make this estimate nonphysical, that is, its degree of polarization (DOP) may be larger than 1. Taking into account the constraint that the estimate must be physically realizable is known to improve the quality of estimation for the Stokes vector [4][5][6][7][8]. The improvement of the estimation quality obtained by taking into account the physical realizability constraint is also found to be valid for the Mueller matrix [5,[9][10][11].…”

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]. However, the work of Valenzuela and Fessler does not account for physical admissibility constraints, and Sfikas et al's algorithm requires a preprocessing step that may blur the edges.…”

Recovery of polarimetric Stokes images by spatial mixture models

“…One of the objectives of the present work is to relax this hypothesis. Stokes restoration estimators were also proposed in [5]. While the latter model covers spatial coherence and edge preservation, a number of related parameters have to be finetuned empirically.…”