Wavelet Image Restoration Using Multifractal Priors

TL;DR

This paper introduces a wavelet-based Bayesian image restoration method that improves computational efficiency and captures multifractal properties, enhancing the recovery of textural details in images.

Contribution

It extends previous Fourier-based methods to wavelet bases, enabling better local property adaptation and multifractal analysis in image restoration.

Findings

Efficient wavelet-based Bayesian restoration method developed.

Enhanced recovery of textural and multifractal image features.

Applicable to medical imaging and other complex image contexts.

Abstract

Bayesian image restoration has had a long history of successful application but one of the limitations that has prevented more widespread use is that the methods are generally computationally intensive. The authors recently addressed this issue by developing a method that performs the image enhancement in an orthogonal space (Fourier space in that case) which effectively transforms the problem from a large multivariate optimization problem to a set of smaller independent univariate optimization problems. The current paper extends these methods to analysis in another orthogonal basis, wavelets. While still providing the computational efficiency obtained with the original method in Fourier space, this extension allows more flexibility in adapting to local properties of the images, as well as capitalizing on the long history of developments for wavelet shrinkage methods. In addition, wavelet methods, including empirical Bayes specific methods, have recently been developed to effectively capture multifractal properties of images. An extension of these methods is utilized to enhance the recovery of textural characteristics of the underlying image. These enhancements should be beneficial in characterizing textural differences such as those occurring in medical images of diseased and healthy tissues. The Bayesian framework defined in the space of wavelets provides a flexible model that is easily extended to a variety of imaging contexts.