The goal of this work is to develop a new theoretical framework for modeling ultrasound images. The hypothesis to be tested is that the rf echo follows an alpha-stable distribution with alpha less or equal to two. This distribution has never been used in modeling the ultrasound rf echo. The Gaussian model, which has been used widely, is a special case of the alpha-stable model with alpha=2. The validity of the model will be tested based on clinical ultrasound images of the breast and phantom data. Based on the alpha-stable model parameters novel tissue characterization features will be devised. The new model will be compared to the K- distribution, which has been proposed for the envelope of the rf echo, strengths and weaknesses of each model will be identified, and their roles in tissue characterization will be compared. Potential improvements in tumor detection by combining the features derived from the two models will also be investigated. Since, in theory, alpha-stable processes with alpha<2 do not have finite moments of order greater or equal to 2, conventional second or high-order statistics-based tools cannot be employed in processing. New methods to model such processes will be developed and applied on image distortion estimation and deconvolution, targeting image resolution enhancement.
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