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

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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 novel method to spatially adapt the regularization parameter; it also 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 image restoration corrupted with Poisson noise. Moreover, 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 and that spatially adapts its regularization parameter within the TV framework.01/2011; - [Show abstract] [Hide abstract]

**ABSTRACT:**At the NIST Neutron Imaging Facility, we collect neutron projection data for both the dry and wet states of a Proton-Exchange-Membrane (PEM) fuel cell. Transmitted thermal neutrons captured in a scintillator doped with lithium-6 produce scintillation light that is detected by an amorphous silicon detector. Based on joint analysis of the dry and wet state projection data, we reconstruct a residual neutron attenuation image with a Penalized Likelihood method with an edge-preserving Huber penalty function that has two parameters that control how well jumps in the reconstruction are preserved and how well noisy fluctuations are smoothed out. The choice of these parameters greatly influences the resulting reconstruction. We present a data-driven method that objectively selects these parameters, and study its performance for both simulated and experimental data. Before reconstruction, we transform the projection data so that the variance-to-mean ratio is approximately one. For both simulated and measured projection data, the Penalized Likelihood method reconstruction is visually sharper than a reconstruction yielded by a standard Filtered Back Projection method. In an idealized simulation experiment, we demonstrate that the cross validation procedure selects regularization parameters that yield a reconstruction that is nearly optimal according to a root-mean-square prediction error criterion.IEEE Transactions on Nuclear Science 01/2013; 60(5):3945-3954. · 1.22 Impact Factor - [Show abstract] [Hide abstract]

**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.04/2011;

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