Specifics and overview of the study

A VRX CT scanner was, by definition, an imaging system. Its spatial resolution, therefore, could be described within the conceptual framework developed in the previous chapter. However, because of the unique design of this device compared with

conventional CT systems, several specific features of the scanner had to be considered when describing its spatial resolution.

First, the VRX CT scanner, in its exact interpretation, only partly satisfied the linearity and shift-invariance conditions required for the spatial-resolution analysis on the basis of transfer theory (Section 4.1). There was no problem with linearity – when

employing a solid-state VRX detector, whose response had been found linear in the range

* _{Sections 5.3-5.5 of this chapter adapted with permission. R. Melnyk and}

F. A. DiBianca, “Modeling and measurement of the detector presampling MTF of a variable resolution x-ray CT scanner,” Med. Phys. 34, 1062-1075, 2007.

of exposures typically used for spatial-resolution measurements,33,40 this requirement was easily met, and no additional linearization of the scanner was needed. But the situation was different with the shift-invariance condition. The VRX CT scanner was not shift- invariant over the entire object plane. The main reason for this included angulation of the VRX detector. Because of the angulation, combined with the fan-beam geometry of the scanner, the cells at different positions from the detector vertex produced different responses when imaging the same object. Another reason was the discrete nature of the VRX detector. This property led to the same shift-variance that is often observed in digital imaging systems (Section 4.3). Despite the mentioned difficulties, the shift-

invariance condition for the VRX CT scanner was approximated by considering each cell separately and then presenting the overall response of the scanner as a function of the cell position. Thus, with the latter approximation, both transfer-theory requirements were satisfied, and the resolution properties of the scanner were analyzed in terms of the previously established measures of spatial resolution.

Next, the VRX CT scanner, according to its underlying principle, provided a resolution increase in the scan (x-y) direction only. The type of the scanner presented in the current study also employed a 1D detector, which was sufficient for proper

implementation of the VRX detection technique (Section 3.1). Consequently, at the detector level, spatial resolution was described using 1D measures (the LSF and 1D MTF). The same 1D measures were also chosen to characterize spatial resolution near the center of the final, reconstructed image, as this resolution was believed to be isotropic.

Another specific feature of the VRX CT scanner was an asymmetrical response from each detector cell. This resulted, again, from the angulation of the VRX detector.

Due to the angulation, there was a difference between the left and right tails of the corresponding LSF. Clearly, such LSF asymmetry would affect the phase information in the spatial-frequency domain. Although the phase content of the scanner spatial

resolution was not separately considered, the effect of the LSF asymmetry on the detector MTF was carefully examined.

Finally, the VRX CT scanner exhibited larger noise variations and might be subjected to slightly more noise at small FOVs than conventional CT systems. The stochastic nature of this noise, however, was generally ignored, and the resolution properties of the scanner were described by the parameters representing only the

expectation values of the selected spatial-resolution measures. The sole statistical effects accounted for in the study were simple variations among different samples of the same parameters.

In an overview, the goal of the current study was a comprehensive evaluation of spatial resolution in the VRX CT scanner. Two components of this resolution were considered – the pre-reconstruction (before image reconstruction) spatial resolution and the post-reconstruction (after image reconstruction) spatial resolution. The post-

reconstruction spatial resolution was chosen for the evaluation because of the importance of this parameter from the clinical point of view. Indeed, this type of spatial resolution described the quality of an image at the final stage of the scanner imaging chain; that image would be used by a radiologist to make a clinical decision. The pre-reconstruction spatial resolution, on the other hand, was selected for the evaluation because of its significance from the engineering point of view. Specifically, the pre-reconstruction spatial resolution characterized the performance of the VRX detector itself, without

influence of the reconstruction algorithm; this parameter, therefore, provided better understanding of the resolution improvement resulting from the detector angulation.

Both components of spatial resolution of the VRX CT scanner were evaluated in terms of the MTF. Based on the MTF hierarchy developed in the previous chapter (Fig. 4.2), the post-reconstruction spatial resolution was represented by the scanner reconstruction MTF. The choice of a measure for the pre-reconstruction spatial resolution was less obvious. Among the three available options – the detector presampling MTF, the system presampling MTF, and the scanner digital MTF – the first measure was selected, due to its advantages when describing inherent spatial resolution of discrete detectors (Section 4.3). Hence, the pre-reconstruction spatial resolution of the VRX CT scanner was given by the detector presampling MTF. On the whole, the detector presampling MTF and the scanner reconstruction MTF were the two component-specific measures of spatial resolution evaluated in the study.

An initial intention was to determine each MTF via both modeling and measurement, and then compare the results to asses the adequacy of the modeling approach. The two distinct ways to obtain the same measure would also provide means for result verification. This idea was successfully realized for the detector presampling MTF, which was modeled by the Monte Carlo technique and measured by the moving- slit method. In the case of the scanner reconstruction MTF, however, the computation of this function from the modeled detector presampling MTF, as originally planned, was found to be difficult. Therefore, the scanner reconstruction MTF was only measured, using the LSF-phantom method.