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Bayesian estimation of regularization and point spread function parameters for Wiener-Hunt deconvolution
François Orieux1, Jean-François Giovannelli, Thomas Rodet
1Laboratoire des Signaux et Systèmes (CNRS-SUPELEC-Univ. Paris-Sud 11), SUPELEC, Plateau de Moulon,3 rue Joliot-Curie, 91 192 Gif-sur-Yvette, France. orieux@lss.supelec.fr
Summary
This study introduces a Bayesian method for image deconvolution, accurately estimating the point spread function (PSF) and hyperparameters. The approach effectively restores high frequencies and spatial details in images.
Area of Science:
- Image processing
- Computational imaging
- Bayesian inference
Background:
- Image deconvolution is crucial for restoring image quality.
- Accurate estimation of the point spread function (PSF) and hyperparameters is challenging.
- Existing methods may lack a unified approach for joint parameter estimation.
Purpose of the Study:
- To develop a Bayesian framework for joint estimation of PSF parameters and hyperparameters in image deconvolution.
- To provide a globally coherent approach for image restoration.
- To enhance the accuracy of deconvolution techniques.
Main Methods:
- Utilized a Bayesian framework with a global a posteriori law for unknown parameters and object.
- Employed a Monte Carlo Markov chain (MCMC) algorithm to compute the posterior mean estimate.
- Performed efficient computations in the Fourier domain.
Main Results:
- Achieved precise estimates for PSF parameters and hyperparameters.
- Demonstrated accurate image restoration, including high frequencies and spatial details.
- Validated the method's effectiveness on simulated examples.
Conclusions:
- The proposed Bayesian method offers a robust and coherent approach to image deconvolution.
- Accurate joint estimation of PSF parameters and hyperparameters leads to superior image restoration.
- The Fourier domain computation enhances efficiency and effectiveness.
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