Task-based detectability and angular-sampling bounds on spatial resolution in cone-beam micro-CT: a closed-form...

Spatial resolution in preclinical cone-beam micro-CT is conventionally characterised by image-domain metrics measured on a specific reconstruction of a specific phantom. Such metrics conflate resolution loss originating in the data (photon noise, angular undersampling) with resolution loss originating in the reconstruction (apodization, regularisation, voxel grid), and do not answer how much room is left for improvement on a given dataset.

To derive and evaluate two reconstruction-independent resolution limits for preclinical cone-beam micro-CT, a photon-noise limit from the projection-domain signal-known-exactly, background-known-exactly (SKE/BKE) ideal observer with the Rose criterion, and an angular-sampling limit from the Crowther criterion, and combine them into a single spatially varying picture that bounds what any classical reconstruction can achieve from a given scan.

We derived closed-form expressions for the photon-noise minimum detectable disc diameter and an off-axis fan-beam extension, and combined them with the Crowther criterion via pointwise minimum. All resolution limits are theoretical evaluations of these closed forms for the geometry of a representative preclinical micro-CT scanner. The only experimentally measured input is the unattenuated photon count per pixel, estimated from two flat-field projections, and the exposure and projection-count sweeps are hypothetical formula inputs, not acquired scans. The closed forms were validated by Poisson Monte Carlo simulation, and the specimen detectability map by fan-beam forward projection of a previously acquired mouse attenuation map. The optimum split of a fixed total photon budget was derived analytically.

The combined limit yields a closed-form scan-design optimum. For the disc-detection task, the maximum worst-case spatial frequency scales as the cube root of the total photon budget per detector pixel (per-view flux times number of views), and an analytic rule sets how to split that budget between flux and views. The off-axis bound follows a "bowl" geometry rising from the centre to the rim, and the parametric sweeps show how each acquisition parameter reshapes this map. Simulated detectability agrees with the closed forms within 1% in minimum detectable diameter, on- and off-axis, and forward-projected real anatomy shifts the photon-noise limit by only $+3$ to $+8\%$ , confirming the uniform specimen model is conservative.

The two reconstruction-independent limits combine into a usable engineering picture for scan design and detectability prediction in preclinical cone-beam micro-CT. The photon-noise limit is a task-based detectability threshold for a specified feature and contrast, expressed in frequency units rather than as a Fourier cutoff, and the combined map is a practical summary of these two independent, necessary constraints. Reconstructions that incorporate strong signal priors may exceed the Crowther limit at the cost of relying on those priors, but cannot exceed the photon-noise limit at any cost. An accompanying open-source interactive web calculator (https://ubc-ford-lab.github.io/ideal_observer_SKE_BKE_model/) implements these bounds for arbitrary scanner geometries.