In this paper we propose a new method for evaluating image recording strategies for limited angle tomography. In limited angle tomography exact three-dimensional （3-D） reconstruction is not achievable. With this met...In this paper we propose a new method for evaluating image recording strategies for limited angle tomography. In limited angle tomography exact three-dimensional （3-D） reconstruction is not achievable. With this method a metric for the reachable reconstruction quality by defined X-ray source trajectories is calculated. The result of our method is independent of reconstruction algorithms. Our approach is based on the gradients of the scanned volume and their grade of determinability. Compared to simulated reconstruction accuracy with simultaneous algebraic reconstruction techniques, the method of evaluation shows the same dependencies on X-ray source trajectories. By using the proposed method different source trajectories for a limited angle range are comparable with respect to the reachable reconstruction quality.展开更多
If a spatial-domain function has a finite support,its Fourier transform is an entire function.The Taylor series expansion of an entire function converges at every finite point in the complex plane.The analytic continu...If a spatial-domain function has a finite support,its Fourier transform is an entire function.The Taylor series expansion of an entire function converges at every finite point in the complex plane.The analytic continuation theory suggests that a finite-sized object can be uniquely determined by its frequency components in a very small neighborhood.Trying to obtain such an exact Taylor expansion is difficult.This paper proposes an iterative algorithm to extend the measured frequency components to unmeasured regions.Computer simulations show that the proposed algorithm converges very slowly,indicating that the problem is too ill-posed to be practically solvable using available methods.展开更多
基金Supported by the German Federal Ministry of Education and Research (No.01EZ0839)
文摘In this paper we propose a new method for evaluating image recording strategies for limited angle tomography. In limited angle tomography exact three-dimensional （3-D） reconstruction is not achievable. With this method a metric for the reachable reconstruction quality by defined X-ray source trajectories is calculated. The result of our method is independent of reconstruction algorithms. Our approach is based on the gradients of the scanned volume and their grade of determinability. Compared to simulated reconstruction accuracy with simultaneous algebraic reconstruction techniques, the method of evaluation shows the same dependencies on X-ray source trajectories. By using the proposed method different source trajectories for a limited angle range are comparable with respect to the reachable reconstruction quality.
基金This research is partially supported by NIH,No.R15EB024283.
文摘If a spatial-domain function has a finite support,its Fourier transform is an entire function.The Taylor series expansion of an entire function converges at every finite point in the complex plane.The analytic continuation theory suggests that a finite-sized object can be uniquely determined by its frequency components in a very small neighborhood.Trying to obtain such an exact Taylor expansion is difficult.This paper proposes an iterative algorithm to extend the measured frequency components to unmeasured regions.Computer simulations show that the proposed algorithm converges very slowly,indicating that the problem is too ill-posed to be practically solvable using available methods.
