Robust non-homomorphic approach for speckle reduction in medical ultrasound images

Most existing wavelet-based image denoising techniques are developed for additive white Gaussian noise. In applications to speckle reduction in medical ultrasound (US) images, the traditional approach is first to perform the logarithmic transform (homomorphic processing) to convert the multiplicative speckle noise model to an additive one, and then the wavelet filtering is performed on the log-transformed image, followed by an exponential operation. However, this non-linear operation leads to biased estimation of the signal and increases the computational complexity of the filtering method. To overcome these drawbacks, an efficient, non-homomorphic technique for speckle reduction in medical US images is proposed. The method relies on the true characterisation of the marginal statistics of the signal and speckle wavelet coefficients. The speckle component was modelled using the generalised Nakagami distribution, which is versatile enough to model the speckle statistics under various scattering conditions of interest in medical US images. By combining this speckle model with the generalised Gaussian signal first, the Bayesian shrinkage functions were derived using the maximum a posteriori (MAP) criterion. The resulting Bayesian processor used the local image statistics to achieve soft-adaptation from homogeneous to highly heterogeneous areas. Finally, the results showed that the proposed method, named GNDShrink, yielded a signal-to-noise ratio (SNR) gain of 0.42 dB over the best state-of-the-art despeckling method reported in the literature, 1.73 dB over the Lee filter and 1.31 dB over the Kaun filter at an input SNR of 12.0 dB, when tested on a US image. Further, the visual comparison of despeckled US images indicated that the new method suppressed the speckle noise well, while preserving the texture and organ surfaces.