Title: Bayesian image analysis in transformed spaces
Authors: Karl Young - University of California San Francisco (United States)
John Kornak - University of California, San Francisco (United States) [presenting]
Abstract: Bayesian image analysis can improve image quality, by balancing a priori expectations of image characteristics, with a model for the noise process via Bayes Theorem. We will give a reformulation of the conventional Bayesian image analysis paradigm in Fourier and wavelet spaces, e.g. for Fourier space the prior and likelihood are given in terms of spatial frequency signals. By specifying the Bayesian model in transformed spaces, spatially correlated priors, that are relatively difficult to model and compute in conventional image space, can be efficiently modeled as a set of independent processes across; the priors are modeled as independent over the transformed space, but tied together by defining a ``parameter function'' over the space for the values of the pdf parameters. The originally inter-correlated and high-dimensional problem in image space is thereby broken down into a series of (trivially parallelizable) independent one-dimensional problems. We will describe the Bayesian image analysis in transformed space modeling approach, illustrate its computational efficiency and speed, and demonstrate useful properties such as isotropy and resolution invariance to model specification which are difficult to obtain in the conventional formulation. We will describe applications in medical imaging, and contrast with results using conventional Bayesian image analysis models. Finally, we will showcase a Python package that is under development to make the approach widely accessible.