## Variational Dirichlet Blur Kernel Estimation

## Abstract

Blind image deconvolution involves two key objectives: 1) latent image and 2) blur estimation. For latent image estimation, we propose a fast deconvolution algorithm, which uses an image prior of nondimensional Gaussianity measure to enforce sparsity and an undetermined boundary condition methodology to reduce boundary artifacts. For blur estimation, a linear inverse problem with normalization and nonnegative constraints must be solved. However, the normalization constraint is ignored in many blind image deblurring methods, mainly because it makes the problem less tractable. In this paper, we show that the normalization constraint can be very naturally incorporated into the estimation process by using a Dirichlet distribution to approximate the posterior distribution of the blur. Making use of variational Dirichlet approximation, we provide a blur posterior approximation that considers the uncertainty of the estimate and removes noise in the estimated kernel. Furthermore, experiments with synthetic and real data demonstrate that the proposed method is very competitive to the state-of-the-art blind image restoration methods.

- Authors:

- Beihang Univ., Beijing (China)
- Univ. de Granada, Granada (Spain)
- Northwestern Univ., Evanston, IL (United States)

- Publication Date:

- Research Org.:
- Northwestern Univ., Evanston, IL (United States). Center for Catalysis and Surface Science

- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA), Office of Nonproliferation and Verification Research and Development (NA-22)

- OSTI Identifier:
- 1487984

- Grant/Contract Number:
- NA0002520

- Resource Type:
- Accepted Manuscript

- Journal Name:
- IEEE Transactions on Image Processing

- Additional Journal Information:
- Journal Volume: 24; Journal Issue: 12; Journal ID: ISSN 1057-7149

- Publisher:
- IEEE

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICS AND COMPUTING; blind deconvolution; image deblurring; variational distribution approximations; Dirichlet distribution; constrained optimization; point spread function; inverse problem

### Citation Formats

```
Zhou, Xu, Mateos, Javier, Zhou, Fugen, Molina, Rafael, and Katsaggelos, Aggelos K. Variational Dirichlet Blur Kernel Estimation. United States: N. p., 2015.
Web. doi:10.1109/TIP.2015.2478407.
```

```
Zhou, Xu, Mateos, Javier, Zhou, Fugen, Molina, Rafael, & Katsaggelos, Aggelos K. Variational Dirichlet Blur Kernel Estimation. United States. doi:10.1109/TIP.2015.2478407.
```

```
Zhou, Xu, Mateos, Javier, Zhou, Fugen, Molina, Rafael, and Katsaggelos, Aggelos K. Mon .
"Variational Dirichlet Blur Kernel Estimation". United States. doi:10.1109/TIP.2015.2478407. https://www.osti.gov/servlets/purl/1487984.
```

```
@article{osti_1487984,
```

title = {Variational Dirichlet Blur Kernel Estimation},

author = {Zhou, Xu and Mateos, Javier and Zhou, Fugen and Molina, Rafael and Katsaggelos, Aggelos K.},

abstractNote = {Blind image deconvolution involves two key objectives: 1) latent image and 2) blur estimation. For latent image estimation, we propose a fast deconvolution algorithm, which uses an image prior of nondimensional Gaussianity measure to enforce sparsity and an undetermined boundary condition methodology to reduce boundary artifacts. For blur estimation, a linear inverse problem with normalization and nonnegative constraints must be solved. However, the normalization constraint is ignored in many blind image deblurring methods, mainly because it makes the problem less tractable. In this paper, we show that the normalization constraint can be very naturally incorporated into the estimation process by using a Dirichlet distribution to approximate the posterior distribution of the blur. Making use of variational Dirichlet approximation, we provide a blur posterior approximation that considers the uncertainty of the estimate and removes noise in the estimated kernel. Furthermore, experiments with synthetic and real data demonstrate that the proposed method is very competitive to the state-of-the-art blind image restoration methods.},

doi = {10.1109/TIP.2015.2478407},

journal = {IEEE Transactions on Image Processing},

number = 12,

volume = 24,

place = {United States},

year = {2015},

month = {9}

}

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