Statistical properties of logarithmically transformed speckle

In synthetic aperture radar (SAR) image processing and analysis, the logarithmic transform is often employed to convert the multiplicative speckle model to an additive noise model. However, this nonlinear operation totally changes the statistics of SAR images. In this communication, we first review the statistical properties of speckle noise in both the intensity and the amplitude formats. Then, we derive the probability density functions, the mean values, and the variances to characterize the log-transformed speckle. Finally we discuss the problems introduced by the logarithmic transform on statistical analysis of SAR images. The statistical models developed in this communication will facilitate subsequent SAR image processing tasks based on the additive noise model.