Presampling, algorithm factors, and noise: considerations for CT in particular and for medical imaging in general.

CT scanners acquire noisy data at discrete sample positions. Typically, a convention of how to continue these data from discrete integer positions to the continuous domain must be applied during processing. We study the properties of three typical one-dimensional spatial domain interpolation algorithms in terms of a cost or quality factor Q. This figure of merit Q is a function of spatial resolution, data noise, and dose and is used to optimize detector design. Spatial resolution R is defined as either mean square width delta or as the full width at half maximum W of the point spread function (PSF). Our results show that a trapezoidal interpolation algorithm is optimal for the high resolution domain (relative to the detector aperture size g) and should be replaced by a triangular or Gaussian interpolation function for spatial resolutions of about 1.3g or larger; these result in bell-shaped PSFs. Assuming such a hybrid algorithm we find a 1.5-fold increase of Q2-this is equivalent to 50% improved dose usage-when smoothing the data to a spatial resolution of 3g or more compared to a highest resolution reconstruction. Therefore it is advisable to use detectors of one-third of the size of the desired spatial resolution W and to compensate for the 1.5-fold increase in Q2 by reducing dose by 33%. Under the presence of moderately sized septa (e.g., 10% of the spatial resolution element size) the benefit of optimizing still lies in the order of 30% improved dose usage; in that case the detector size g should be on the order of W/2 and a dose reduction of 23% can be achieved. Again, bell-shaped PSFs show a better tradeoff between noise and resolution for a given dose than rectangular-shaped PSFs. The general interpretation of our results is that the degree of freedom of choosing the weighting or interpolation function for a given resolution is large for small detectors and small for large detectors. Thus systems with small g have a higher potential of optimization compared to systems with large g. Similarly, detector binning, which corresponds to replacing g by 2g, should be avoided. Note that the figures reported correspond to a one-dimensional interpolation. Two-dimensional detectors typically separate and resulting quality factors can be easily obtained by multiplication. Then, Q2 is expected to improve by a factor of 1.52 without septa and by a factor of 1.32 with septa. This indicates that dose can be reduced by about 56% and about 41%, respectively. Our findings are general and not restricted to CT. They can be readily applied to medical or nonmedical imaging devices and digital detectors and they may also turn out to be useful in other fields.