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This book addresses imaging of the heart with retrospectively gated helical cone beam computed tomography (CT). It includes a chapter on the theory of CT reconstruction, familiarising the reader with the problem of cone beam reconstruction. The Extended Cardiac Reconstruction (ECR) framework is presented for heart-rate-adaptive gated helical cardiac CT reconstruction. Reconstruction assessment criteria such as the temporal resolution, the homogeneity in terms of the cardiac phase and the smoothness at cycle-to-cycle transitions are developed. Several novel reconstruction optimisation approaches are described: An approach for the heart-rate-adaptive optimisation of the temporal resolution is presented. Streak artifacts at cycle-to-cycle transitions can be minimised by using an improved cardiac weighting scheme. The optimal quiescent cardiac phase for the reconstruction can be determined automatically with the motion map technique. Results for all optimisation procedures applied toECR are presented and discussed based on patient and phantom data. An extensive simulation study evaluates the ECR performance for systems with larger detectors.