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

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.

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    ABSTRACT: We propose a flexible and computationally efficient method to solve the non-homogeneous Poisson (NHP) model for grayscale and color images within the TV framework. The NHP model is relevant to image restoration in several applications, such as PET, CT, MRI, etc. The proposed algorithm uses a quadratic approximation of the negative log-likelihood function to pose the original problem as a non-negative quadratic programming problem. The reconstruction quality of the proposed algorithm outperforms state of the art algorithms for grayscale im-age restoration corrupted with Poisson noise. Furthermore, it places no prohibitive restriction on the forward operator, and to best of our knowledge, the proposed algorithm is the only one that explicitly includes the NHP model for color images within the TV framework.
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