Wavelet Image Restoration Using Multifractal Priors
Karl Young, John Kornak, Eric Friedman

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,…
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Taxonomy
TopicsImage and Signal Denoising Methods · Medical Image Segmentation Techniques · Grey System Theory Applications
