**6. Conclusion**

In this chapter, a despeckling method, based on a 2D directional non separable transform known as contourlet transform is presented. Conventional 2D wavelet transform is separable and thus cannot sparsely represent non separable structures of the image, such as directional curves. It is found that pyramidal directional filter bank feature of contourlet transform makes it a good choice for representation of curves and edges in the image. But, the contourlet transform, one of the recent geometrical image transforms, lacks the feature of translation invariance due to sub sampling in its filter bank structure. In cycle spinning, CT is improved by averaging the estimation of all translations of the degraded image. The Gibbs effect is considerably reduced by the contourlet transform with cycle spinning, because the average of different estimations of the image reduces the oscillations. In the literature, the authors [33,41,45,54,55,61] have considered ultrasound images (natural/synthetic) with artificially added speckle noise content and have proposed methods for despeckling such images. However, in the present study, we considered ultrasound images captured by the ultrasound equipment which contain inherent speckle noise and have proposed methods for removing the speckle noise more effectively.

When the noise characteristics of the images are unknown, it is proposed to denoise by a linear regression model, which is cost effective compared to the other methods. We have proposed a novel linear regression model for Gaussian noise estimation and removal in despeckling medical ultrasound images. The experimental results demonstrate its efficacy both in terms of speckle reduction and computational time required for denoising. Further, the proposed regression model is simple, generic and computationally inexpensive. Hence, it is easily amenable for building embedded system software for ultrasound imaging equipments in order to display the high quality images, which help the medical experts for speedy accurate image analysis and diagnosis. Further, the proposed regression model is simple, generic and computationally inexpensive.
