Asymptotic confidence intervals for Poisson regression
Journal of Multivariate Analysis
Proceedings of the 13th ACM SIGKDD international conference on Knowledge discovery and data mining
A proximal iteration for deconvolving Poisson noisy images using sparse representations
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
Restoration of Poissonian images using alternating direction optimization
IEEE Transactions on Image Processing
Multiscale Photon-Limited Spectral Image Reconstruction
SIAM Journal on Imaging Sciences
A Novel Sparsity Reconstruction Method from Poisson Data for 3D Bioluminescence Tomography
Journal of Scientific Computing
Poisson image denoising using geometric platelets and geometric quadlets
Signal Processing
A New Poisson Noise Filter Based on Weights Optimization
Journal of Scientific Computing
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This paper describes a statistical multiscale modeling and analysis framework for linear inverse problems involving Poisson data. The framework itself is founded upon a multiscale analysis associated with recursive partitioning of the underlying intensity, a corresponding multiscale factorization of the likelihood (induced by this analysis), and a choice of prior probability distribution made to match this factorization by modeling the “splits” in the underlying partition. The class of priors used here has the interesting feature that the “noninformative” member yields the traditional maximum-likelihood solution; other choices are made to reflect prior belief as to the smoothness of the unknown intensity. Adopting the expectation-maximization (EM) algorithm for use in computing the maximum a posteriori (MAP) estimate corresponding to our model, we find that our model permits remarkably simple, closed-form expressions for the EM update equations. The behavior of our EM algorithm is examined, and it is shown that convergence to the global MAP estimate can be guaranteed. Applications in emission computed tomography and astronomical energy spectral analysis demonstrate the potential of the new approach