Bayesian Image Analysis in Fourier Space

• Activity Number: 59
• Type: Topic Contributed
• Date/Time: Sunday, August 3, 2014 : 4:00 PM to 5:50 PM
• Sponsor: Section on Statistics in Imaging
• Author(s): John Kornak*+
• Companies: University of California, San Francisco
• Keywords: Bayesian image analysis ; Fourier space ; Image priors ; Markov random fields

Abstract

Bayesian image analysis provides a solution for improving image quality relative to deterministic methods, such as linear filtering, by balancing a priori expectations of image characteristics with a model for the noise process. We will here give a reformulation of the conventional Bayesian image analysis paradigm in Fourier space, i.e., such that the prior and likelihood are defined in terms of probability densities across spatial frequencies. Spatially correlated priors, that are relatively difficult to model and compute in conventional image space, can often be more efficiently modeled as a set of independent processes across Fourier space. The originally inter-correlated and high-dimensional problem in image space is thereby broken down into a series of independent one-dimensional problems (using 'parameter functions' to capture variation in the model's prior parameters over Fourier space). The Fourier space independence definition leads to easy model specification and relatively fast and direct computation that is on the order of that for deterministic filtering methods. We will give specific examples of applications, and contrast with Markov random field based models.