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

Describes a previous 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 SNR ₀, 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.