Bayesian Image Analysis in Fourier Space

Bayesian image analysis has been instrumental for over 40 years in addressing challenges such as image noise reduction, de-blurring, feature enhancement, and object detection. Despite its success, modeling spatial dependencies inherent to these problems often results in significant computational challenges. This work introduces the Bayesian Image Analysis in Fourier Space (BIFS) framework, which redefines conventional Bayesian modeling for continuous-valued images by transforming the problem into the Fourier domain. This transformation reduces the original high-dimensional dependent estimation problem into multiple low-dimensional, independent subproblems in Fourier space. The BIFS approach thereby simplifies computation while enabling flexible model specification, efficient formulation of isotropic priors, adaptability to diverse prior expectations, and invariance to changes in image resolution. BIFS thus offers a powerful and computationally efficient framework for a wide range of imaging applications. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.