A physically based, probabilistic model for ultrasonic images incorporating shape, microstructure, and system characteristics.

Abstract

Recent successes with Bayesian methods for analysis of shape in medical images have motivated our development of a shape-based data likelihood for ultrasound, the foundation of which is a computationally feasible, pixel-based, probabilistic image model. Previous probabilistic models for ultrasound generally assume an analytic form, e.g., Rayleigh, Rician, K, Generalized K, etc., then attempt to fit data to the model. Assumptions and intensive computation inherent in such an approach make it unsuitable for our purposes. In the pursuit of a new model, we have described previously a physical model for image formation that incorporates the imaging system characteristics, the surface shape, and the surface microstructure. That physical model was validated via a visual comparison of simulated and actual images of a cadaveric vertebra. In this work, a random phasor sum representation of the physical model provides the basis for a probabilistic form. In contrast to existing probabilistic models, we compute the amplitude mean and variance directly from the physical model. These statistics can be displayed as images to characterize the tissue, but, more importantly, they permit the subsequent assignment of a suitable density function to each pixel for the purposes of constructing a data likelihood. The order of these steps, i.e., first computing the statistics and then assigning a density function, permits the inclusion of the local surface shape, the surface microstructure, and the system characteristics at every image pixel without violating the physical model. Currently, the value of the SNR0, the ratio of the mean to the standard deviation, is used to estimate whether a pixel is Rayleigh- or non-Rayleigh-distributed. This assessment forms the basis for a data likelihood constructed as a product of Rayleigh and Gaussian density functions describing the individual image pixels.