Statistical properties of an unassisted image quality index for SAR imagery

The ℳ estimator is a recently proposed image-quality index used to evaluating despeckling operation in SAR (synthetic aperture radar) data. It is used also to rank despeckling filters and also to improve their designs. As a difference with traditional image-quality estimators, it operates not on the filtered result but on a derived one (ratio image). However, a deep statistical analysis of its properties has not been done yet. In this work, we focus on obtaining insights of its distribution as well on exploring other remarkable statistical properties of this unassisted estimator. This studio is performed through the well-known ANOVA (analysis of variance) technique. We test our analysis on a set of synthetic and actual SAR data and provide some guides to enrich the ℳ estimator to extend its capabilities.