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Poisson Image Reconstruction With Total Variation Regularization

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Abstract

This paper describes an optimization framework for reconstructing nonnegative image intensities from linear projections contaminated with Poisson noise. Such Poisson inverse problems arise in a variety of applications, ranging from medical imaging to astronomy. A total variation regularization term is used to counter the ill-posedness of the inverse problem and results in reconstructions that are piecewise smooth. The proposed algorithm sequentially approximates the objective function with a regularized quadratic surrogate which can easily be minimized. Unlike alternative methods, this approach ensures that the natural nonnegativity constraints are satisfied without placing prohibitive restrictions on the nature of the linear projections to ensure computational tractability. The resulting algorithm is computationally efficient and outperforms similar methods using wavelet-sparsity or partition-based regularization.

Citation

R. M. Willett, Z. T. Harmany and R. F. Marcia, “Poisson image reconstruction with total variation regularization”, in IEEE International Conference on Image Processing (ICIP), 2010, 4177–4180.

BibTeX

@inproceedings{willett-icip2010-poissontv,
  doi = {10.1109/ICIP.2010.5649600},
  title = {Poisson image reconstruction with total variation regularization},
  author = {Willett, Rebecca M. and Harmany, Zachary T. and Marcia, Roummel F.},
  booktitle = {IEEE International Conference on Image Processing (ICIP)},
  month = {sep},
  year = {2010},
  pages = {4177–4180},
  abstract = {This paper describes an optimization framework for reconstructing nonnegative image intensities from linear projections contaminated with Poisson noise. Such Poisson inverse problems arise in a variety of applications, ranging from medical imaging to astronomy. A total variation regularization term is used to counter the ill-posedness of the inverse problem and results in reconstructions that are piecewise smooth. The proposed algorithm sequentially approximates the objective function with a regularized quadratic surrogate which can easily be minimized. Unlike alternative methods, this approach ensures that the natural nonnegativity constraints are satisfied without placing prohibitive restrictions on the nature of the linear projections to ensure computational tractability. The resulting algorithm is computationally efficient and outperforms similar methods using wavelet-sparsity or partition-based regularization.}
}