5 research outputs found
Fixing Nonconvergence of Algebraic Iterative Reconstruction with an Unmatched Backprojector
We consider algebraic iterative reconstruction methods with applications in
image reconstruction. In particular, we are concerned with methods based on an
unmatched projector/backprojector pair; i.e., the backprojector is not the
exact adjoint or transpose of the forward projector. Such situations are common
in large-scale computed tomography, and we consider the common situation where
the method does not converge due to the nonsymmetry of the iteration matrix. We
propose a modified algorithm that incorporates a small shift parameter, and we
give the conditions that guarantee convergence of this method to a fixed point
of a slightly perturbed problem. We also give perturbation bounds for this
fixed point. Moreover, we discuss how to use Krylov subspace methods to
efficiently estimate the leftmost eigenvalue of a certain matrix to select a
proper shift parameter. The modified algorithm is illustrated with test
problems from computed tomography
Fixing nonconvergence of algebraic iterative reconstruction with an unmatched backprojector
\u3cp\u3eWe consider algebraic iterative reconstruction methods with applications in image reconstruction. In particular, we are concerned with methods based on an unmatched projector/backprojector pair, i.e., the backprojector is not the exact adjoint or transpose of the forward projector. Such situations are common in large-scale computed tomography, and we consider the common situation where the method does not converge due to the nonsymmetry of the iteration matrix. We propose a modified algorithm that incorporates a small shift parameter, and we give the conditions that guarantee convergence of this method to a fixed point of a slightly perturbed problem. We also give perturbation bounds for this fixed point. Moreover, we discuss how to use Krylov subspace methods to efficiently estimate the leftmost eigenvalue of a certain matrix to select a proper shift parameter. The modified algorithm is illustrated with test problems from computed tomography.\u3c/p\u3
Fixing nonconvergence of algebraic iterative reconstruction with an unmatched backprojector
We consider algebraic iterative reconstruction methods with applications in image reconstruction. In particular, we are concerned with methods based on an unmatched projector/backprojector pair, i.e., the backprojector is not the exact adjoint or transpose of the forward projector. Such situations are common in large-scale computed tomography, and we consider the common situation where the method does not converge due to the nonsymmetry of the iteration matrix. We propose a modified algorithm that incorporates a small shift parameter, and we give the conditions that guarantee convergence of this method to a fixed point of a slightly perturbed problem. We also give perturbation bounds for this fixed point. Moreover, we discuss how to use Krylov subspace methods to efficiently estimate the leftmost eigenvalue of a certain matrix to select a proper shift parameter. The modified algorithm is illustrated with test problems from computed tomography