Joint Optimization of Collimator and Reconstruction Parameters in X-Ray Fluorescence Computed Tomography Using Analytical Point Spread Function and Model Observer

Objective: To jointly optimize collimator design and image reconstruction algorithm in X-ray Fluorescence Computed Tomography (XFCT) for imaging low concentrations of high atomic number (Z) elements in small animal models. Methods: Single pinhole (SPH) collimator and three types of multi-pinhole (MPH) collimators were evaluated. MPH collimators with 5, 7, and 9 pinholes using lead, stainless steel and brass were considered. A digital cylindrical phantom (0.5 mm3 voxels) of 25 mm diameter and 25 mm height with a central 5 mm diameter and 12.5 mm height cylindrical insert containing gold nanoparticles (2:1 insert: background concentration) was modeled. A 125 kVp, 2 mm Sn filtered x-ray spectrum (0.5 cGy/projection) for gold K-shell XFCT was considered. System matrices were implemented using analytical point spread functions (PSF) for each pinhole collimator. Poisson noise was added to the projection data (16 equiangular views) before image reconstruction using Maximum-Likelihood Expectation-Maximization (ML-EM) algorithm. Signal-present and signal-absent images were generated for the detection task performed by a channelized Hotelling observer (CHO) with 10 Dense Difference-of-Gaussian channels. The area under the curve (AUC) in receiver operating characteristic was used as the image quality metric. Results: A stainless steel focusing type MPH with 7 pinholes and 20 iterations of ML-EM provided the highest AUC. Conclusion: MPH collimators outperformed SPH collimators for XFCT and consistently high AUCs were observed with focusing type MPH designs with 7 pinholes. Significance: The combinations of collimator design and image reconstruction parameters that maximized AUC were identified, which could improve the performance of XFCT.