Necessary and sufficient convergence conditions for algebraic image reconstruction algorithms
IEEE Transactions on Image Processing
AIR Tools - A MATLAB package of algebraic iterative reconstruction methods
Journal of Computational and Applied Mathematics
Generalized projections onto convex sets
Journal of Global Optimization
An acceleration scheme for cyclic subgradient projections method
Computational Optimization and Applications
Preconditioned iterative regularization in Banach spaces
Computational Optimization and Applications
Journal of Parallel and Distributed Computing
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We propose and study a block-iterative projection method for solving linear equations and/or inequalities. The method allows diagonal componentwise relaxation in conjunction with orthogonal projections onto the individual hyperplanes of the system, and is thus called diagonally relaxed orthogonal projections (DROP). Diagonal relaxation has proven useful in accelerating the initial convergence of simultaneous and block-iterative projection algorithms, but until now it was available only in conjunction with generalized oblique projections in which there is a special relation between the weighting and the oblique projections. DROP has been used by practitioners, and in this paper a contribution to its convergence theory is provided. The mathematical analysis is complemented by some experiments in image reconstruction from projections which illustrate the performance of DROP.