The SOund Navigation And Ranging (SONAR) images are perturbed by speckle noise. This paper presents a new denoising method in the wavelet domain, which tends to reduce the speckle, preserving the structural features and the textural information of the scene. Shift invariance associated with good directional selectivity is important for the use of a wavelet transform (WT) in denoising of SONAR images. In this paper, we propose the use of a variant

Throughout recent years, many Wavelet Transforms (WTs) were used in digital image processing: the Discrete WT (DWT), the Stationary WT (SWT) or the Hyperanalytic WT (HWT). All these transforms have in common a feature, the Mother Wavelets (MW) used. A great number of MWs was already proposed in literature. The purpose of this paper is the selection of the MW for hyperanalytic Bayesian image denoising on the basis of its space-frequency localization.