Image reconstruction performance as a function of model complexity using information geometry: Application to transmission tomographic imaging

Models used to derive image reconstruction algorithms typically make assumptions designed to increase the computational tractability of the algorithms while taking enough account of the physics to achieve desired performance. As the models for the physics become more detailed, the algorithms typically increase in complexity, often due to increases in the number of parameters in the models. When parameters are estimated from measured data and models of increased complexity include those of lower complexity as special cases, then as the number of parameters increases, model errors decrease and estimation errors increase. We adopt an information geometry approach to quantify the loss due to model errors and Fisher information to quantify the loss due to estimation errors. These are unified into one cost function. This approach is detailed in an X-ray transmission tomography problem where all models are approximations to the underlying problem defined on the continuum. Computations and simulations demonstrate the approach. The analysis provides tools for determining an appropriate model complexity for a given problem and bounds on information that can be extracted.