Purpose: Design and optimization of medical imaging systems benefit from accurate theoretical modeling that identifies the physical factors governing image quality, particularly in the early stages of system development. This work extends Fourier metrics of imaging performance and detectability index ͑dЈ͒ to tomosynthesis and cone-beam CT ͑CBCT͒ and investigates the extent to which dЈ is a valid descriptor of task-based imaging performance as assessed by human observers. Methods:The detectability index for tasks presented in 2D slices ͑d slice Ј ͒ was derived from 3D cascaded systems analysis of tomosynthesis and CBCT. Anatomical background noise measured in a physical phantom presenting power-law spectral density was incorporated in the "generalized" noise-equivalent quanta. Theoretical calculations of d slice Ј were performed as a function of total angular extent ͑ tot ͒ of source-detector orbit ranging 10°-360°under two acquisition schemes: ͑i͒ Constant angular separation between projections ͑constant-⌬͒, giving variable number of projections ͑N proj ͒ and dose vs tot and ͑ii͒ constant number of projections ͑constant-N proj ͒, giving constant dose ͑but variable angular sampling͒ with tot . Five simple observer models were investigated: Prewhitening ͑PW͒, prewhitening with eye filter and internal noise ͑PWEi͒, nonprewhitening ͑NPW͒, nonprewhitening with eye filter ͑NPWE͒, and nonprewhitening with eye filter and internal noise ͑NPWEi͒. Human observer performance was measured in 9AFC tests for five simple imaging tasks presented within uniform and power-law clutter backgrounds. Measurements ͑from 9AFC tests͒ and theoretical calculations ͑from cascaded systems analysis of d slice Ј ͒ were compared in terms of area under the ROC curve ͑A z ͒ Results: Reasonable correspondence between theoretical calculations and human observer performance was achieved for all imaging tasks over the broad range of experimental conditions and acquisition schemes. The PW and PWEi observer models tended to overestimate detectability, while the various NPW models predicted observer performance fairly well, with NPWEi giving the best overall agreement. Detectability was shown to increase with tot due to the reduction of out-of-plane clutter, reaching a plateau after a particular tot that depended on the imaging task. Depending on the acquisition scheme, however ͑i.e., constant-N proj or ⌬͒, detectability was seen in some cases to decline at higher tot due to tradeoffs among quantum noise, background clutter, and view sampling. Conclusions: Generalized detectability index derived from a 3D cascaded systems model shows reasonable correspondence with human observer performance over a fairly broad range of imaging tasks and conditions, although discrepancies were observed in cases relating to orbits intermediate to 180°and 360°. The basic correspondence of theoretical and measured performance supports the 1754 1754 Med. Phys. 38 "4…,

The complex tradeoffs among anatomical background, quantum noise, and electronic noise in projection imaging, tomosynthesis, and CBCT can be described by generalized cascaded systems analysis, providing a useful framework for system design and optimization.

Purpose: Nonstationarity is an important aspect of imaging performance in CT and cone-beam CT (CBCT), especially for systems employing iterative reconstruction. This work presents a theoretical framework for both filtered-backprojection (FBP) and penalized-likelihood (PL) reconstruction that includes explicit descriptions of nonstationary noise, spatial resolution, and task-based detectability index. Potential utility of the model was demonstrated in the optimal selection of regularization parameters in PL reconstruction. Methods: Analytical models for local modulation transfer function (MTF) and noise-power spectrum (NPS) were investigated for both FBP and PL reconstruction, including explicit dependence on the object and spatial location. For FBP, a cascaded systems analysis framework was adapted to account for nonstationarity by separately calculating fluence and system gains for each ray passing through any given voxel. For PL, the point-spread function and covariance were derived using the implicit function theorem and first-order Taylor expansion according to Fessler ["Mean and variance of implicitly defined biased estimators (such as penalized maximum likelihood): Applications to tomography," IEEE Trans. Image Process. 5(3), 493-506 (1996)]. Detectability index was calculated for a variety of simple tasks. The model for PL was used in selecting the regularization strength parameter to optimize task-based performance, with both a constant and a spatially varying regularization map. Results: Theoretical models of FBP and PL were validated in 2D simulated fan-beam data and found to yield accurate predictions of local MTF and NPS as a function of the object and the spatial location. The NPS for both FBP and PL exhibit similar anisotropic nature depending on the pathlength (and therefore, the object and spatial location within the object) traversed by each ray, with the PL NPS experiencing greater smoothing along directions with higher noise. The MTF of FBP is isotropic and independent of location to a first order approximation, whereas the MTF of PL is anisotropic in a manner complementary to the NPS. Task-based detectability demonstrates dependence on the task, object, spatial location, and smoothing parameters. A spatially varying regularization "map" designed from locally optimal regularization can improve overall detectability beyond that achievable with the commonly used constant regularization parameter. Conclusions: Analytical models for task-based FBP and PL reconstruction are predictive of nonstationary noise and resolution characteristics, providing a valuable framework for understanding and optimizing system performance in CT and CBCT.