Adaptative regularization parameter for Poisson noise with a bilevel approach: application to spectral computerized tomography

DOI10.1080/17415977.2020.1864348OpenAlexW3116505171MaRDI QIDQ5036759

Bruno Sixou

Publication date: 23 February 2022

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

Full work available at URL: https://doi.org/10.1080/17415977.2020.1864348

zbMATH Keywords

inverse problemsregularization parameterPoisson noiseKullback-LeiblerX-ray imaging

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Convex functions and convex programs in convex geometry (52A41) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20) Numerical solution to inverse problems in abstract spaces (65J22)

Related Items (1)

Bilevel Methods for Image Reconstruction

Uses Software

• AIR tools

Cites Work

• Poisson inverse problems
• A theoretical framework for the regularization of Poisson likelihood estimation problems
• The Radon transform
• Optimal selection of the regularization function in a weighted total variation model. I: Modelling and theory
• Applied functional analysis. Main principles and their applications
• AIR tools -- a MATLAB package of algebraic iterative reconstruction methods
• A discrepancy principle for Poisson data
• Convergence rates in expectation for Tikhonov-type regularization of inverse problems with Poisson data
• Regularization parameter selection methods for ill-posed Poisson maximum likelihood estimation
• Spatially adapted regularization parameter selection based on the local discrepancy function for Poissonian image deblurring
• Joint additive Kullback–Leibler residual minimization and regularization for linear inverse problems
• Efficient gradient projection methods for edge-preserving removal of Poisson noise
• Convergence of Best Entropy Estimates
• Maximum Entropy Regularization for Fredholm Integral Equations of the First Kind
• Poisson intensity estimation for tomographic data using a wavelet shrinkage approach
• A new look at entropy for solving linear inverse problems
• Regularization of ill-posed problems in Banach spaces: convergence rates
• On Information and Sufficiency
• Nonlinear partial differential equations with applications
• Convex analysis and monotone operator theory in Hilbert spaces
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