For material identification, characterization, and quantification, it is useful to estimate system-independent material properties that do not depend on the detailed specifications of the X-ray computed tomography (CT) system such as spectral response. System independent ρe and Ze (SIRZ) refers to a suite of methods for estimating the system independent material properties of electron density (ρe) and effective atomic number (Ze) of an object scanned using dual-energy X-ray CT (DECT). The current state-of-the-art approach, SIRZ-2, makes certain approximations that lead to inaccurate estimates for large atomic numbered (Ze) materials. In this paper, we present an extension, SIRZ-3, which iteratively reconstructs the unknown ρe and Ze while avoiding the limiting approximations made by SIRZ-2. Unlike SIRZ-2, this allows SIRZ-3 to accurately reconstruct ρe and Ze even at large Ze. SIRZ-3 relies on the use of a new non-linear differentiable forward measurement model that expresses the DECT measurement data as a direct analytical function of ρe and Ze. Leveraging this new forward model, we use an iterative optimization algorithm to reconstruct (or solve for) ρe and Ze directly from the DECT data. Compared to SIRZ-2, we show that the magnitude of performance improvement using SIRZ-3 increases with increasing values for Ze.
4D X-ray computed tomography (4D-XCT) is widely used to perform non-destructive characterization of time varying physical processes in various materials. The conventional approach to improving temporal resolution in 4D-XCT involves the development of expensive and complex instrumentation that acquire data faster with reduced noise. It is customary to acquire data with many tomographic views at a high signal to noise ratio. Instead, temporal resolution can be improved using regularized iterative algorithms that are less sensitive to noise and limited views. These algorithms benefit from optimization of other parameters such as the view sampling strategy while improving temporal resolution by reducing the total number of views or the detector exposure time. This paper presents the design principles of 4D-XCT experiments when using regularized iterative algorithms derived using the framework of model-based reconstruction. A strategy for performing 4D-XCT experiments is presented that allows for improving the temporal resolution by progressively reducing the number of views or the detector exposure time. Theoretical analysis of the effect of the data acquisition parameters on the detector signal to noise ratio, spatial reconstruction resolution, and temporal reconstruction resolution is also presented in this paper.
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