Unified snr analysis of medical imaging systems

Abstract

The ideal observer signal to noise ratio (snr) has been derived from statistical decision theory for all of the major medical imaging modalities. This snr provides an absolute scale for image system performance assessment and leads to instrumentation design goals and constraints for imaging system optimisation since no observer can surpass the performance of the ideal observer. The dependence of detectable detail size on exposure or imaging time follows immediately from the analysis. A framework emerges for comparing data acquisition techniques, e.g. reconstruction from projections versus Fourier methods in nmr imaging, and time of flight positron emission tomography (tofpet) versus conventional pet. The approach of studying the ideal observer is motivated by measurements on human observers which show that they can come close to the performance of the idea) observer, except when the image noise has negative correlations-as in images reconstructed from projections-where they suffer a small but significant penalty.

Figure 1

Distribution of filter outputs when s₂ is present (left) and when s₁ is present (right plotted against the tiller output. C, decision criterion; d, separation of means of the two distributions in units of their common standard deviation.

Figure 2

Low contrast Gaussian signals ΔN, Δρ and ΔV above background level N (or ρ or V). RMS radius equals σ. (See also notations used in table 2.)

Figure 3

neq(f) spectrum for second generation ct system.

Figure 4

Geometry for planar integrals in 3D planar projection-reconstruction imaging. In practice there are many planes, more closely spaced. (See also figure 5). The diameter is D.

Figure 5

Geometry for calculations in Appendices 3 and 4.