  The goal of this thesis is to provide a framework for the use of task-based
metrics of image quality to aid in the design, implementation, and evaluation
of CT image reconstruction algorithms and CT systems in general. We support the
view that task-based metrics of image quality can be useful in guiding the
algorithm design and implementation process in order to yield images of
objectively superior quality and higher utility for a given task. Further, we
believe that metrics such as the Hotelling observer (HO) SNR can be used as
summary scalar metrics of image quality for the evaluation of images produced
by novel reconstruction algorithms. In this work, we aim to construct a concise
and versatile formalism for image reconstruction algorithm design,
implementation, and assessment. The bulk of the work focuses on linear
analytical algorithms, specifically the ubiquitous filtered back-projection
(FBP) algorithm. However, due to the demonstrated importance of
optimization-based algorithms in a wide variety of CT applications, we devote
one chapter to the characterization of noise properties in TV-based iterative
reconstruction, as the understanding of image statistics in optimization-based
reconstruction is the limiting factor in applying HO metrics.
