# Statistical elimination of boundary artefacts in image deblurring

@article{Calvetti2005StatisticalEO, title={Statistical elimination of boundary artefacts in image deblurring}, author={Daniela Calvetti and Erkki Somersalo}, journal={Inverse Problems}, year={2005}, volume={21}, pages={1697 - 1714} }

The goal of image deconvolution is to restore an image within a given area, from a blurred and noisy specimen. It is well known that the convolution operator integrates not only the image in the field of view of the given specimen, but also part of the scenery in the area bordering it. The result of a deconvolution algorithm which ignores the non-local properties of the convolution operator will be a restored image corrupted by distortion artefacts. These artefacts, which tend to be more…

## 22 Citations

### Bayesian image deblurring and boundary effects

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Two different approaches to treat the non-locality of the convolution operator are considered: one is to estimate the image extended outside the field of view, and the other is to Treat the influence of the out of view scenery as boundary clutter.

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- Geology2008 15th IEEE International Conference on Image Processing
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This paper establishes new boundary conditions by smoothly expanding the input image to a large tile, which helps reducing the boundary discontinuities and accordingly makes all restoration filters based on Fast Fourier Transform not produce obvious image border artifacts.

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A large number of techniques have been developed to cope with an original image which has been degraded due to the imperfections in the acquisition system: blurring and noise, most of them under the regularization or the Bayesian frameworks.

### Improved image deblurring with anti-reflective boundary conditions and re-blurring

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A cross-scale constraint is proposed to make the sharp image correspond to a good local minimum and the iterative residual deconvolution approach is adopted to trap the MAP approach in the desired local minimum, which constrains the solution from coarse to fine.

### Statistical Methods in Imaging

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Basic principles for the construction of priors and likelihoods are presented, together with a discussion of numerous computational statistics algorithms, including Maximum Likelihood estimators, Maximum A Posteriori and Conditional Mean estimator, Expectation Maximization, Markov chain Monte Carlo, and hierarchical Bayesian models.

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The paper discusses inverse problems in which the unknown is a function that is assumed to be piecewise smooth with discontinuities of unknown location and size. If the locations of the…

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