Statistical and Entropy Considerations for Ultrasound Tissue Characterization

Modern cancerous tumor diagnostics is nearly impossible without invasive
methods, such as biopsy, that may require involved surgical procedures. In recent years
some work has been done to develop alternative non-invasive methods of medical
diagnostics. For this purpose, the data obtained from an ultrasound image of the body crosssection,
has been analyzed using statistical models, including Rayleigh, Rice, Nakagami,
and K statistical distributions. The homodyned-K (H-K) distribution has been found to be
a good statistical tool to analyze the envelope and/or the intensity of backscattered signal
in ultrasound tissue characterization. However, its use has usually been limited due to the
fact that its probability density function (PDF) is not available in closed-form. In this work
we present a novel closed-form representation for the H-K distribution. In addition, we propose using the first order approximation of the H-K distribution, the I-K distribution
that has a closed-form, for the ultrasound tissue characterization applications. More
specifically, we show that some tissue conditions that cause the backscattered signal to
have low effective density values, can be successfully modeled by the I-K PDF. We
introduce the concept of using H-K PDF-based and I-K PDF-based entropies as additional
tools for characterization of ultrasonic breast tissue images. The entropy may be used as a
goodness of fit measure that allows to select a better-fitting statistical model for a specific
data set. In addition, the values of the entropies as well as the values of the statistical
distribution parameters, allow for more accurate classification of tumors.