Abstract
Classical tomohraphic methods for image reconstruction are constructed based on the assumption that projection data were obtained by integration over infinitely thin lines. However, a detector receiving a signal in a real experiment always has a certain width and, in a more general case, a nonzero angular aperture specified by a collimator. A modified iterative algorithm on the basis of the Neumann technique is proposed that makes it possible to take the actual system of signal recording in the process of reconstruction into account. The computational experiment is carried out on a model simulating local two-dimensional distributions of emission coefficients. Modification of the algorithm consists in the utilization of nonlinear relaxation and regularizing cubic splines. This makes it possible to stabilize the iteration process and to avoid a loss in accuracy when the noise level in projection data increases. The algorithm is also stable to certain parameters variations of the geometry of collection of projection data. The results of reconstruction by using the method proposed here are compared with the results of operation of the classical method of tomography—the method of inverse projection with filtering (Shepp-Logan filter).
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