Regularized estimation of Stokes images from polarimetric measurements

Abstract

In the remote sensing context the goal of imaging polarimetry is to map the state of polarization of a scene of interest. The polarization state of a scene can be represented by the Stokes parameters. Since the Stokes parameters are not directly measurable one must first make several individual measurements and then the infer the Stokes parameters. We approach the Stokes parameter construction problem using penalized-likelihood estimation. Given the measured linearly polarized images, what is the optimal means by which to deblur and denoise and construct the Stokes parameters? In traditional image restoration one attempts to restore the blurred and noise corrupted data directly. In the case of imaging polarimetry we must answer the question of the optimality of restoring the measured data and then forming the Stokes images or restoring the Stokes images directly. An alternative approach is to estimate the Stokes parameters directly. We define our cost function for reconstruction by a weighted least squares data fit penalty 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 Stokes parameters directly leads to somewhat lower error.

Joint reconstruction of Stokes images from polarimetric measurements

“…,y J ͒. Penalized-likelihood, or maximum a posteriori (MAP), estimators have been used extensively for such image reconstruction problems [7][8][9][10]. A penalizedlikelihood estimator for ⌫ is given by…”

“…The degrading effect of the imaging system is taken to be optical blur and represented by the matrix B, i.e., A j = B in Eq. (10). This matrix is Toeplitz if the system is shift invariant, but the analysis that follows applies to a general B matrix.…”