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August 2019 Spatially adaptive Bayesian image reconstruction through locally-modulated Markov random field models
Salem M. Al-Gezeri, Robert G. Aykroyd
Braz. J. Probab. Stat. 33(3): 498-519 (August 2019). DOI: 10.1214/18-BJPS399

Abstract

The use of Markov random field (MRF) models has proven to be a fruitful approach in a wide range of image processing applications. It allows local texture information to be incorporated in a systematic and unified way and allows statistical inference theory to be applied giving rise to novel output summaries and enhanced image interpretation. A great advantage of such low-level approaches is that they lead to flexible models, which can be applied to a wide range of imaging problems without the need for significant modification.

This paper proposes and explores the use of conditional MRF models for situations where multiple images are to be processed simultaneously, or where only a single image is to be reconstructed and a sequential approach is taken. Although the coupling of image intensity values is a special case of our approach, the main extension over previous proposals is to allow the direct coupling of other properties, such as smoothness or texture. This is achieved using a local modulating function which adjusts the influence of global smoothing without the need for a fully inhomogeneous prior model. Several modulating functions are considered and a detailed simulation study, motivated by remote sensing applications in archaeological geophysics, of conditional reconstruction is presented. The results demonstrate that a substantial improvement in the quality of the image reconstruction, in terms of errors and residuals, can be achieved using this approach, especially at locations with rapid changes in the underlying intensity.

Citation

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Salem M. Al-Gezeri. Robert G. Aykroyd. "Spatially adaptive Bayesian image reconstruction through locally-modulated Markov random field models." Braz. J. Probab. Stat. 33 (3) 498 - 519, August 2019. https://doi.org/10.1214/18-BJPS399

Information

Received: 1 June 2017; Accepted: 1 April 2018; Published: August 2019
First available in Project Euclid: 10 June 2019

zbMATH: 07094814
MathSciNet: MR3960273
Digital Object Identifier: 10.1214/18-BJPS399

Rights: Copyright © 2019 Brazilian Statistical Association

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Vol.33 • No. 3 • August 2019
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