<title>Homomorphic wavelet shrinkage and feature emphasis for speckle reduction and enhancement of echocardiographic images</title>

Abstract

An approach for speckle reduction and feature enhancement under a framework of multiscale wavelet analysis is presented. The advantages of both soft thresholding and hard thresholding wavelet shrinkage techniques are utilized to eliminate noise and preserve the sharpness of salient features. We integrate a method of wavelet shrinkage with nonlinear processing to enhance contrast within structures and along object boundaries. Feature restoration and enhancement are accomplished by modifying the gain of a signal's variational energy. In this study, we focus on multiplicative noise, such as speckle noise. We show that this algorithm is capable of enhancing features of interest, such as endocardial and epicardial boundaries in 2-D short-axis echocardiograms while at the same time reducing speckle. Speckle is modeled as multiplicative noise, and approximated by additive stationary Gaussian white noise on a logarithmic scale. In our algorithm, shrinkage of wavelet coefficients via soft thresholding within finer scales is carried out on coefficients of logarithmically transformed echocardiograms. Nonlinear feature emphasis combined with hard thresholding within middle levels of transform space are performed subsequently on wavelet coefficients. The first operation reduces speckle while the second step accomplishes structure and object boundary enhancement. Preliminary results suggest that the algorithm can remove speckle noise and enhance contrast along boundaries of importance to cardiologists. We have applied this algorithm to echocardiograms of varying quality, and present both experimental analysis and sample results.