Quantitative image‐based spectral reconstruction for computed tomography

Computed tomography (CT) devices are routinely employed to obtain three‐dimensional images of the human body. The reconstructed CT numbers represent weighted x‐ray attenuation coefficients. Their spectral weighting is influenced by the selected x‐ray source spectrum, the detector characteristics, and the attenuating object itself. The quantitative ground truth of the scanned object is given by the spectral attenuation coefficient. It is not directly measurable in standard CT. For spectral CT measurements, algorithms like the basis material decomposition yield parametrized representations of the spectral mass attenuation coefficient. In practical applications, image‐based formulations are commonly used. They are affected by both the CT system characteristics and the object self‐attenuation effects. In this article the authors introduce an image‐based spectral CT method. It expresses measured CT data as a spectral integration of the spectral attenuation coefficient multiplied by a local weighting function (LWF). The LWF represents the local energy weighting in the image domain, taking into account the system and reconstruction properties and the object self‐attenuation. A generalized image‐based formulation of spectral CT algorithms is obtained, with no need for additional corrections of, e.g., beam hardening. The iterative procedure called local spectral reconstruction yields both the mass attenuation coefficients of the object and a representation of the LWF. The quantitative accuracy and precision of the method are investigated in several applications: First, beam hardening corrections to various target energy weightings and attenuation correction maps for SPECT/CT and PET/CT are calculated. Second, an iodine density evaluation is performed. Finally, a direct identification of spectral attenuation functions using the LWF result is demonstrated. In all applications, the ground truth of the objects is reproduced with a quantitative accuracy in the subpercent to 2% range. An exponential convergence behavior of the iterative procedure is observed, with one to two iteration steps as a good compromise between quantitative accuracy and precision. The authors conclude that the method can be used to perform image‐based spectral CT reconstructions with quantitative accuracy. Existing algorithms benefit from the intrinsic treatment of beam hardening and system properties. Novel algorithms are enabled to directly compare material model functions to spectral measurement data.