A Weibull‐distribution‐based hybrid total variation method for speckle reduction in ultrasound images

Abstract

Speckle reduction is still an intractable task in ultrasound imaging field. Ultrasound speckle is usually described as multiplicative noise with its statistics following a Rayleigh or Gaussian distribution. To employ these two distributions effectively, the authors attempt to describe ultrasound speckle using a Weibull distribution, because it can include the Rayleigh distribution as a special case and also approximate a Gaussian distribution by varying its shape and scale parameters. The authors’ contribution in this paper is to propose a Weibull-distribution-based hybrid total variation (WHTV) method to reduce ultrasound speckle. The WHTV energy functional is convex and consists of a new data fidelity term and a new regularization term. The former is derived from the multiplicative Weibull model of ultrasound speckle based on the maximum likelihood criterion. The latter is a new edge-weighted combination of the first- and second-order total variation, with the advantage of preserving edges while alleviating the staircase effects. The minimization of the WHTV energy functional is implemented by the split Bregman algorithm. Experimental results on synthetic and real ultrasound images have demonstrated not only that the Weibull distribution is a better fitting model for the statistics of ultrasound speckle than other distributions such as Rayleigh, Gaussian, Gamma, and Nakagami, but also that the proposed WHTV method can achieve better despeckling performance than several state-of-the-art variational methods.