The paper presented here describes a new practical approach to the reconstruction problem applied to 3D spiral x-ray tomography. The concept we propose is based on a continuous-to-continuous data model, and the reconstruction problem is formulated as a shift invariant system. This original reconstruction method is formulated taking into consideration the statistical properties of signals obtained by the 3D geometry of a CT scanner. It belongs to the class of nutating reconstruction methods and is based on the advanced single slice rebinning (ASSR) methodology. The concept shown here significantly improves the quality of the images obtained after reconstruction and decreases the complexity of the reconstruction problem in comparison with other approaches. Computer simulations have been performed, which prove that the reconstruction algorithm described here does indeed significantly outperforms conventional analytical methods in the quality of the images obtained.

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This paper is closely related to the originally formulated 3D statistical model-based iterative reconstruction algorithm for spiral cone-beam x-ray tomography. The concept proposed here is based on a continuous-to-continuous data model, and the reconstruction problem is formulated as a shift invariant system. This algorithm significantly improves the quality of the subsequently reconstructed images, so allowing a reduction in the x-ray dose absorbed by a patient. This form of reconstruction problem permits a reduction in the computational complexity in comparison with other model-based iterative approaches. Computer simulations have shown that the reconstruction method presented here outperforms standard FDK methods with regard to the image quality obtained and can be competitive in terms of time of calculation.

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This paper presents some practical realizations of image reconstruction methods for spiral cone-beam tomography scanners in which an X-ray tube with a flying focal spot is used. These methods are related to the original formulated 3D statistical model-based iterative reconstruction approach for tomography with flying focal spot. The conception proposed here is based on principles of a statistical model-based iterative reconstruction (MBIR) methodology, where the reconstruction problem is formulated as a shift-invariant system (a continuousto-continuous data model). We adopted nutating reconstruction-based approaches, i.e. the advanced single slice rebinning methodology (usually applied in CT scanners with X-ray tubes with a flying focal spot), and a procedure compliant with the FDK scheme. We showed that our methods significantly improve the quality of obtained images compared to the traditional FBP algorithms. Consequently, it can allow for a reduction in the x-ray dose absorbed by a patient. Additionally, we show that our approach can be competitive in terms of the time of calculations, especially if we consider commercially used statistical reconstruction systems.