Multiplicative and product model constraints upon speckle filtering of SAR images

Speckle filter performances depend strongly on the speckle and scene models used as the basis for filter development. These models that incorporate implicitly certain assumptions on speckle, scene and observed signals, were generally adopted and used without any justification. In this study, the multiplicative and the product speckle models, which have been used as the basis for the development of the most well known filters, are analyzed. Their implicits assumptions are discussed with regards to the stationarity-nonstationarity of speckle, observed and scene signals. Two categories of speckle filters are distinguished as a function of the stationarity-nonstationary assumption on speckle random variations. The various approximate models used for the multiplicative speckle noise model are then assessed as functions of speckle and scene characteristics. The S. N. Madsen method (1987) was extended to the various models to derive the requirements on scene signal variations for the validity of the multiplicative stationary speckle model, and the product model which forces speckle to be a nonstationary process