Synthetic aperture sonar (SAS) is actively used in sea bed imagery. Indeed high resolution images provided by SAS are of great interest, especially for the detection, localization and eventually classification of objects lying on sea bed. SAS images are highly corrupted by a granular multiplicative noise, called speckle noise which reduces spatial and radiometric resolutions. The purpose of this article is to present a new adaptive processing that allows image filtering, for both the additive and multiplicative noise case. This new process is based on the marriage between a multi-resolution transformation and a filtering method. The filtering technique used here is based on the two-dimensional stochastic matched filtering method, which maximizes the signal-to-noise ratio after processing and minimizes mean square error between the signal's approximation and the original one. Results obtained on real SAS data are presented and compared with those obtained using classical processing.