The distribution of the local entropy in ultrasound images

In this article, a model for the amplitude statistics of the backscattered ultrasonic signal is presented. We propose to view a tissue as being composed of a large number of small units, each having slightly different characteristics. This variability within the tissue is expressed by fluctuations in the parameters of the local probability distribution function (PDF). Based on analogous expressions derived for radio propagation and optical scintillations, the local PDF is modulated by a lognormal distribution of the local standard deviation. Integrating the local contributions yields the amplitude PDF for the entire tissue. We show that the local entropy is a normal variable, since for four different local PDFs it is linearly related to the logarithm of the local standard deviation. When the local entropy histogram exhibits distinct and multiple peaks, the local entropy distribution can be used for region segmentation. This fact is demonstrated for ultrasonic images of ovarian cysts.