Computational Methods for Inverse Problems
Computational Methods for Inverse Problems
A Nonnegatively Constrained Convex Programming Method for Image Reconstruction
SIAM Journal on Scientific Computing
Total Variation Processing of Images with Poisson Statistics
CAIP '09 Proceedings of the 13th International Conference on Computer Analysis of Images and Patterns
An Iterative Method for Edge-Preserving MAP Estimation When Data-Noise Is Poisson
SIAM Journal on Scientific Computing
Fast, robust total variation-based reconstruction of noisy, blurred images
IEEE Transactions on Image Processing
Penalized maximum-likelihood image reconstruction using space-alternating generalized EM algorithms
IEEE Transactions on Image Processing
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In positron emission tomography, image data corresponds to measurements of emitted photons from a radioactive tracer in the subject. Such count data is typically modeled using a Poisson random variable, leading to the use of the negative-log Poisson likelihood fit-to-data function. Regularization is needed, however, in order to guarantee reconstructions with minimal artifacts. Given that tracer densities are primarily smoothly varying, but also contain sharp jumps (or edges), total variation regularization is a natural choice. However, the resulting computational problem is quite challenging. In this paper, we present an efficient computational method for this problem. Convergence of the method has been shown for quadratic regularization functions and here convergence is shown for total variation regularization. We also present three regularization parameter choice methods for use on total variation-regularized negative-log Poisson likelihood problems. We test the computational and regularization parameter selection methods on two synthetic data sets.