On the statistical characteristics of log-compressed Rayleigh signals: theoretical formulation and experimental results

Abstract

This paper addresses the effects of nonlinear LOG compression on the amplitude of the backscattered signals. The changes in the statistical characteristics of signals were examined and cornelated with the compression parameters. We develop an analytical formulation for the probability density function (PDF) of logcompressed amplitude signals. To obtain the theoretical F'DF, a Rayleigh distributed signal is subjected to a scaled log-compression of the form nlln(x)+n2. Such transformation is common in medical ulnasound image formation as it allows independent control over the dynamic range and gain of the displayed image. The resulting Fisher-Tippett F' DF and its statistical parameters are derived and compared with the empirically measured statistics of u limages of scattering phantoms. The comparisons reveal a great degree of similarity between theoretical PDF and the histogram of the image, even though the goodness-of-fit tests indicate statistical mismatch from theoretical model due to factors such as non-ideal log compression transfer, noise, envelope smoothing, etc..

In vivo validation of a novel method for regional myocardial wall motion analysis based on echocardiographic tissue tracking

“…Since the DS is measured by a high precision method (sono-micrometry) its deviation reflects mostly the physiological differences between the sheep. However, the GCS deviation is higher than the DS deviation, reflecting additional inaccuracies of the tracking method, probably due to out-of-plane motion of the ROI and the tracking of speckles rather than real reflectors as reported in [7,12].…”

A Multiscale Morphological Approach to Local Contrast Enhancement for Ultrasound Images

“…This nonlinear processing changes the statistical model of the echo signal. After that, it obeys double exponential distribution [8].…”

Optimized GPU Framework for Speckle Reduction Using Histogram Matching and Region Growing

“…First, from [8], we know, mathematically the optimal number of bins to represent a Gaussian distribution with a 95% confidence level is: 2/5 1) -1.87(n = bins of Number (1) And the number of bins could be 8 for n = 49, i.e., from a 7x7 local window. Equation (1) could be used to approximately determine the number of bins of more practical distribution, such as the double exponential from the compressed images [9]. The number of bins derived from Eqn (1) has been assumed for nonzero bins, from which we should group equally the whole range of intensity (e.g., 255 for an 8-bit image), that is to say, 32 bins to have around 8 nonzero bins to represent a discrete histogram in practice.…”