A PDE-Based Nonlinear Filter Adapted to Rayleigh’s Speckle Noise for De-speckling 2D Ultrasound Images

Abstract

The speckle noise present in the acquired ultrasound image may lead to misinterpretation of medical image during diagnosis and therefore, it must be reduced. The speckle noise in ultrasound image is normally multiplicative in nature and distributed according to Rayleigh’s probability density function (pdf). In this paper, a nonlinear partial-differential equation (PDE) based speckle reduction model adapted to Rayleigh’s noise is proposed in variational framework to reduce the speckle noise from 2D ultrasound (US) images. The initial condition of the PDE is the speckle noised US image and the de-speckled image is obtained after certain iterations of the proposed PDE till its convergence. The performance of the proposed non-linear PDE based filter has been evaluated in terms of mean square error (MSE), peak signal-to-noise ratio (PSNR), correlation parameter (CP) and mean structure similarity index map (MSSIM) for several ultrasound images with varying amount of speckle noise variance. The obtained results justify the applicability of the proposed scheme.