Purpose: Nonstationarity of noise poses a major challenge to the modeling and optimization of CT imaging systems, particularly those employing iterative reconstruction. This work presents theoretical models for the spatially varying noise and spatial resolution properties of filtered‐backprojection (FBP) and penalized‐likelihood (PL) reconstruction and provides a method to exploit spatially varying PL regularization to improve task‐based detectability. Methods: A cascaded systems model was adapted to predict the local noise‐power spectrum (NPS) and modulation transfer function (MTF) at each voxel location in FBP by separately calculating the fluence and system gains for each ray passing through the voxel. For PL reconstruction with a quadratic penalty, the implicit function theorem and second‐order Taylor expansion were used to derive the covariance matrix and point spread function, the Fourier transforms of which yield NPS and MTF under assumptions of local stationarity and shift‐invairance, respectively. Detectability index was computed for the non‐prewhitening observer model for simple imaging tasks, including asymmetric tasks corresponding to structures of particular orientation. Spatially‐varying PL regularization maps were designed to control noise and resolution in a manner hypothesized to improve detectability. Results: The NPS in both FBP and PL reconstructions was shown to be anisotropic, spatially‐varying, and object‐dependent, with PL carrying greater spatial variation in MTF due to stronger regularization of projection data in regions of greater attenuation. Complex dependencies were revealed between detectability and the object, spatial location, and regularization. Use of a spatially‐varying PL regularization map improved overall detectability beyond that achievable by constant regularization, with greater advantage observed for asymmetric tasks. Conclusion: The theoretical models successfully predicted local NPS and MTF in both FBP and PL reconstructions. The models demonstrated utility in knowledgeable selection of reconstruction parameters that improve task‐based detectability and provide a valuable guide to the development of CT systems employing conventional and iterative reconstruction methods.
ASJC Scopus subject areas
- Radiology Nuclear Medicine and imaging