Purpose: The development of tomosynthesis imaging systems benefits significantly from a fundamental understanding of noise and resolution and recent developments point to the importance of statistical reconstruction. However the ability to predict imaging performance has been limited by the lack of a closed‐form reconstruction and object‐dependent spatially‐variant results. This work overcomes such barriers though closed‐form approximation of local image properties about the solution to penalized‐likelihood objectives. We incorporate advanced system noise and forward projection models to establish a theoretical basis for predicting imaging performance in tomosynthesis. Methods: Based on previous work general to tomography [Fessier 1996] we derive high‐fidelity approximations of the local impulse response covariance function and noise‐power spectrum (NPS) in x‐ray tomosynthesis. The prediction method does not rely on explicit iterative reconstructions of projection data and includes a general framework for system noise based on cascaded systems analysis of the detection process. Forward models have been developed for both the prediction model and the penalized‐likelihood reconstruction algorithms used to experimentally validate the results. Results: The covariance and NPS in a phantom study included: 1) the approximate prediction approach; and 2) a brute force approach based on iterative reconstruction of ensemble data. Excellent agreement was observed between the two methods. The predictor approach accurately captured the spatially‐variant noise and resolution properties using orders of magnitude less computation time and represents the first application of such a model in tomosynthesis. The results are applied across a broad range of imaging techniques including orbital angle number of projections and dose. Conclusions: Closed‐form predictors of noise and resolution in tomosynthesis by statistical image reconstruction have been developed and validated in comparison to measurement. The approach provides a new theoretical basis for performance characterization in spatially‐variant systems and a tool for optimizing image quality and system design. Research supported by NIH.
ASJC Scopus subject areas
- Radiology Nuclear Medicine and imaging