Tikhonov regularized Poisson likelihood estimation: theoretical justification and a computational method

DOI10.1080/17415970701404235zbMath1258.35206OpenAlexW2148785120MaRDI QIDQ4908303

Johnathan M. Bardsley, N'Djekornom Laobeul

Publication date: 5 March 2013

Published in: Inverse Problems in Science and Engineering (Search for Journal in Brave)

Full work available at URL: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.594.7116

zbMATH Keywords

regularizationmaximum likelihood estimationill-posed problemsimage reconstructionnonnegatively constrained minimization

Mathematics Subject Classification ID

Ill-posed problems for PDEs (35R25) Inverse problems for PDEs (35R30) Stochastic particle methods (65C35)

Related Items (9)

Total variation-penalized Poisson likelihood estimation for ill-posed problems ⋮ Restoring Poissonian images by a combined first-order and second-order variation approach ⋮ An improved Newton projection method for nonnegative deblurring of Poisson-corrupted images with Tikhonov regularization ⋮ Deblurring Poisson noisy images by total variation with overlapping group sparsity ⋮ Techniques for regularization parameter and hyper-parameter selection in PET and SPECT imaging ⋮ A theoretical analysis of L¹ regularized Poisson likelihood estimation ⋮ An analysis of regularization by diffusion for ill-posed Poisson likelihood estimations ⋮ Scaling techniques for gradient projection-type methods in astronomical image deblurring ⋮ Alternating direction method for the high-order total variation-based Poisson noise removal problem

Uses Software

• KELLEY

Cites Work

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• On the Solution of Large Quadratic Programming Problems with Bound Constraints
• Numerical Optimization
• A Nonnegatively Constrained Convex Programming Method for Image Reconstruction
• Computational Methods for Inverse Problems
• A general method to devise maximum-likelihood signal restoration multiplicative algorithms with non-negativity constraints.

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