An evaluation of Bayesian estimators and PDF models for despeckling in the undecimated wavelet domain

Goal of this paper is an evaluation of Bayesian estimators: Minimum Mean Square Error (MMSE), Minimum Mean Absolute Error (MMAE) and Maximum A-posteriori Probability (MAP). Such estimations have been carried out in the undecimated wavelet domain. Bayesian estimation requires probability density function (PDF) models for the wavelet coefficients of the reflectivity and of the signal-dependent noise. In this work several combination of PDFs will be assessed. Closed-form solutions for MMSE, MMAE and MAP have been derived, whenever possible; numerical solutions otherwise. Experimental results carried out on simulated noisy images evidence the cost-performance trade off of the different estimators in conjunction with PDF models. MAP estimation with generalized Gaussian (GG) PDF for wavelet coefficients of both reflectivity and signal-dependent noise (GG - GG) yields best performances. MAP with Laplacian - Gaussian (L - G) is only 0.07 dB less performing than MAP with GG - GG. However, the former admits a closed-form solution and its computational cost is more than ten times lower than that of the latter. Results on true single look high-resolution Cosmo-SkyMed SAR images provided by Italian Space Agency (ASI), are presented and discussed.