Impact of resolution modeling on detectability: Analysis in terms of noise-equivalent quanta

Objectives To quantitatively compare trade-offs posed by resolution modeling (RM) including analysis of lesion or defect detectability in terms of the modulation transfer function (MTF), noise power spectrum (NPS) and noise equivalent quanta (NEQ).

Methods RM methods model resolution-degrading effects within the reconstruction system matrix. Detectability as characterized using inter-class signal-to-noise (SNR; used to estimate area under ROC curve) can be shown to depend on the lesion or defect (O(f) in the Fourier space) and the NEQ spectrum: SNR^2=integ_{f}O(f)NEQ(f)df. Denoting the point response function in the Fourier domain as H(f), i.e. MTF(f)=H(f)/H(0), then NEQ(f)=(H(0)MTF(f))^2/NPS(f) where NPS is Fourier transform of the noise covariance (which we quantify using analytic noise propagation calculations). We characterized the impact of RM on both MTF and NPS, and NEQ and detectability. We simulated Rb-82 myocardial perfusion (with varying transmural defect levels) including effects of positron range, photon noncollinearity, intercrystal penetration & scattering. We performed conventional trade-off analysis (resolution vs. noise as defined spatially (roughness) or across noise realizations (ensemble)), as well as proposed MTF, NPS and NEQ analysis. We also performed numerical channelized Hotelling observer (CHO) studies.

Results Accurate RM can enhance MTF values at low-to-mid frequencies (0-0.2 cycles/voxel) by up to 60%. However, RM also increases inter-voxel correlations, leading to increased NPS values at low-to-mid frequencies (0-0.2 cycles/voxel) by up to 100% though reducing NPS values at higher frequencies. The net result is that NEQ can be degraded at low-to-high-frequencies due to RM, explaining limited improvements in detectability, as also verified using our CHO studies.

Conclusions RM can be more comprehensively analyzed in terms of MTF, NPS and NEQ, explaining why conventional simplistic trade-off curves do not provide a complete picture of the impact of RM and can in fact overestimate its detectability performance.