The multiplicity of sensors used in medical imaging leads to different noises. Non informative noise can damage the image interpretation process and the performance of automatic analysis. The method proposed in this paper allows compensating highly noisy image data from non informative noise without sophisticated modeling of the noise statistics. This generic approach uses jointly a wavelet decomposition scheme and a non-isotropic Total Variation filtering of the transform coefficients. This framework benefits from both the hierarchical capabilities of the wavelet transform and the well-posed regularization scheme of the Total Variation. This algorithm has been tested and validated on test-bed data, as well as different clinical MR and 3D ultrasound images, enhancing the capabilities of the proposed method to cope with different noise models.