Despeckling of medical ultrasound kidney images in the curvelet domain using diffusion filtering and MAP estimation

• An algorithm to reduce speckle has been proposed in the undecimated curvelet domain.
• Maximum A posteriori Probability Technique with the priori probability assumption as Gaussian is used to estimate the shrinkage function.
• Part of the curvelet coefficients are modelled using the estimated shrinkage function, whereas rest of the coefficients are diffusion filtered.
• Proposed method is compared with popular spatial domain filters, wavelet and curvelet domain methods quantitatively.

Speckle remains as a fundamental problem in all coherent imaging modalities such as ultrasound, synthetic aperture radar (SAR) and laser. Presence of speckle gives a granular appearance to the image, hence hinders the details of the underlying object. This paper presents a novel speckle reduction method in the curvelet domain with coefficient modelling and diffusion filtering of the coefficients. An un-decimated Άtrous based curvelet transform of the image is done. A shrinkage function is estimated with the curvelet transformed coefficients using Maximum A posteriori Probability (MAP) technique with the priori distribution assumption as Gaussian. Part of the curvelet coefficients are diffusion filtered using Perona Malik Anisotrpic Diffusion filter (PMAD) and the rest of the coefficients are modelled using the estimated shrinkage function. Proposed algorithm has been tested with the synthetic as well as real time ultrasound kidney images and is found to be effective in removing the speckles. The proposed system is compared with the popular spatial domain filters such as Frost, Kuan and Wiener, also with wavelet and curvelet domain methods. Objective evaluation using peak signal to noise ratio (PSNR), coefficient of correlation (CoC) and structural similarity (SSIM) measures have been done to demonstrate the effectiveness of the proposed system.