Bayesian Adaptive Smoothing for Image Reconstruction

• Activity Number: 58
• Type: Invited
• Date/Time: Monday, August 12, 2002 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Computing*
• Author(s): Robert Aykroyd*+
• Affiliation(s): University of Leeds
• Keywords: Adaptive Smoothing ; Discontinuity priors ; Markov chain Monte Carlo ; Bayesian methods ; Markov random fields ; Prior distributions

Abstract

Recently, the use of homogeneous Gibbs prior models in image processing has become widely accepted. There has been, however, much discussion over precisely which models are most appropriate. For the majority of applications, the simplest Gaussian model tends to oversmooth reconstructions so it has been rejected in favor of various edge-preserving alternatives. The underlying problem, however, is not with the Gaussian family, but with the assumption of homogeneity.

In this paper an inhomogeneous Gaussian random field is proposed as a general prior model for image processing applications. The simplicity of the Gaussian model allows rapid calculation, and the flexibility of the spatially varying prior parameter allows varying degrees of spatial smoothing. This approach is in the spirit of adaptive kernel density methods where only the choice of the variable window width is important.

The analysis of archaeological and medical data is used to illustrate the methods. The proposed procedures lead to more accurate reconstruction, allowing greater flexibility; small features are not masked by the smoothing and, constant regions obtain sufficient smoothing to remove the effects of noise.