On some optimization techniques in image reconstruction from projections
From MaRDI portal
Publication:1109546
DOI10.1016/0168-9274(87)90028-6zbMath0655.65140OpenAlexW2084263592MaRDI QIDQ1109546
Publication date: 1987
Published in: Applied Numerical Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/0168-9274(87)90028-6
Radon transformcomputerized tomographyreconstruction algorithmsentropy maximizationimage reconstruction from projectionsquadratic minimizationexpository paperlikelihood maximization
Special integral transforms (Legendre, Hilbert, etc.) (44A15) Numerical methods for integral transforms (65R10)
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Cites Work
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- Partial inverse of a monotone operator
- SMART - an algorithm for reconstructing pictures from projections
- Connections between the Cimmino-method and the Kaczmarz-method for the solution of singular and regular systems of equations
- A simultaneous projections method for linear inequalities
- An automatic relaxation method for solving interval linear inequalities
- A note on the ART of relaxation
- A relaxed version of Bregman's method for convex programming
- The role of duality in optimization problems involving entropy functionals with applications to information theory
- An iterative row-action method for interval convex programming
- Reconstructing pictures from projections: On the convergence of the ART algorithm with relaxation
- The Radon transform
- On some methods for entropy maximization and matrix scaling
- Iterative algorithms for large partitioned linear systems, with applications to image reconstruction
- New methods for linear inequalities
- An interior points algorithm for the convex feasibility problem
- Strong underrelaxation in Kaczmarz's method for inconsistent systems
- Probability, statistical optics, and data testing. A problem solving approach
- Solution of underdetermined nonlinear equations by stationary iteration methods
- Symmetric duality, and a convergent subgradient method for discrete, linear, constrained approximation problems with arbitrary norms appearing in the objective function and in the constraints
- The X-ray transform
- The defect correction principle and discretization methods
- On the convergence of the discrete ART algorithm for the reconstruction of digital pictures from their projections
- Projection method for solving a singular system of linear equations and its applications
- Convergence of the cyclical relaxation method for linear inequalities
- Practical and mathematical aspects of the problem of reconstructing objects from radiographs
- Decomposition through formalization in a product space
- Optimization of “$\log x$” Entropy over Linear Equality Constraints
- Geometric Programming: Methods, Computations and Applications
- The Relaxation Method for Solving Systems of Linear Inequalities
- Extensions of Hildreth’s Row-Action Method for Quadratic Programming
- Entropy in linear programs
- Row-Action Methods for Huge and Sparse Systems and Their Applications
- Mathematical optimization versus practical performance: A case study based on the maximum entropy criterion in image reconstruction
- Cyclic subgradient projections
- A relaxation method for reconstructing objects from noisy X-rays
- Relaxation methods for image reconstruction
- Properties of Kruithof's Projection Method
- A Statistical Model for Positron Emission Tomography
- A method of iterative data refinement and its applications
- The method of projections for finding the common point of convex sets
- Generalized Iterative Scaling for Log-Linear Models
- The Relaxation Method for Linear Inequalities
- The Relaxation Method for Linear Inequalities
