Conference Paper

Poisson image reconstruction with total variation regularization

Dept. of Electr. & Comput. Eng., Duke Univ., Durham, NC, USA
DOI: 10.1109/ICIP.2010.5649600 Conference: Image Processing (ICIP), 2010 17th IEEE International Conference on
Source: IEEE Xplore


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.

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    • "Additionally imposing prior information on the solution, e.g. that the solutions has a small total variation, leads to an extension of the EM algorithm, e.g. the EM-TV algorithm [4] [10]. See also [5] [30] [31] [37] for related approaches and [10] [11] for extensions of EM-TV to Bregmanized total variation regularization. "
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