The image reconstruction process in emission computed tomography (ECT) is an inverse problem for the photon transport equation. For monochromatic emission sources it is closely related to the inversion of the attenuated Radon transform, a nonlinear ill posed inverse problem. Due to its practical importance for medical diagnostics, this problem has been addressed various times. Here we present the theoretical setting of ECT and discuss some new numerical strategies based on regularization techniques. We include experiments to compare some of the numerical approaches.
Abstract. This work concerns the practical computation of the volumetric modulus, also called normalized volume, of a convex cone in a Euclidean space of dimension beyond three.Deterministic and stochastic techniques are considered.Mathematical subject classification: Primary: 28A75; Secondary: 52A20.
A major step towards quantitative SPECT imaging may be achieved if attenuation, scatter and blurring effects are accounted for in the reconstruction process. Here we consider an approach which simultaneously estimates the unknown attenuation coefficient and the emission source using the emission data only. This leads to an inverse mathematical problem which could no longer be solved via iterative procedures like the well-known EM-algorithm. Instead, a regularization approach based on nonlinear optimization techniques is used. We present a successful strategy of the analytic type, and we test it in a simulated case study.
A major step towards quantitative SPECT imaging may be achieved if attenuation, scatter and blurring effects are accounted for in the reconstruction process. Here we consider an approach which simultaneously estimates the unknown attenuation coefficient and the emission source using the emission data only. This leads to an inverse mathematical problem which could no longer be solved via iterative procedures like the well-known EM-algorithm. Instead, a regularization approach based on nonlinear optimization techniques is used. We present a successful strategy of the analytic type, and we test it in a simulated case study.
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