Speckle Analysis Using Signal to Noise Ratios Based on Fractional Order Moments

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Abstract
The SNR (signal-to-noise ratio) of the echo envelope image is a monotonically-increasing function of scatterer number density. Various SNRs, like amplitude SNR and intensity SNR, can be used to quantify the scatterer density. The problem of using a SNR based on higher order moments like the intensity SNR is that they require large sample sizes to obtain estimates with high confidence (the variance of the estimate becomes large for higher moments). In this paper, we consider SNRs based on fractional order moments (moments of order less than 1), and obtain mathematical analyses of their properties using the K distribution, which has been shown to be a good model for the density function of backscatter echo envelope signal. Statistics of SNRs based on fractional moment are derived and appear to be more robust and useful than the amplitude and intensity SNRs previously studied. The SNRs based on fractional order moments have greater dynamic range and the sample size requirements are smaller than those for integral order moment SNRs, like amplitude SNR or intensity SNR. Thus, SNRs based on fractional order moments could be used to better quantify the variations in scatterer density which can be used for tissue classification problems.