During acquisition, the SONAR images are corrupted by multiplicative noise (speckle).The aim of an image denoising algorithm is then to reduce the noise level, while preserving the image features. There is a great diversity of wavelet based estimators used like denoising systems. The corresponding denoising methods have three steps: the computation of the forward Wavelet Transform (WT); the filtering of the wavelet coefficients; and the computation of the inverse wavelet transform of the result obtained. In the following, the Dual Tree Complex Wavelet Transform (DT-CWT) will be associated with a variant of a maximum a posteriori bishrink filter because its explicit input-output relation permits a sensitivity analysis. The bishrink filter has a high sensitivity with some parameters, especially in the homogeneous regions. The main idea of this paper is to reduce this sensitivity by diversification. In this respect the regions with different homogeneity degrees are identified and in each of them the WT of the acquired image is filtered using a number of different variants of bishrink filters in accordance with its homogeneity.