  This work is to develop a general framework, namely analytical iterative
reconstruction (AIR) method, to incorporate analytical reconstruction (AR)
method into iterative reconstruction (IR) method, for enhanced CT image quality
and reconstruction efficiency. Specifically, AIR is established based on the
modified proximal forward-backward splitting (PFBS) algorithm, and its
connection to the filtered data fidelity with sparsity regularization is
discussed. As a result, AIR decouples data fidelity and image regularization
with a two-step iterative scheme, during which an AR-projection step updates
the filtered data fidelity term, while a denoising solver updates the sparsity
regularization term. During the AR-projection step, the image is projected to
the data domain to form the data residual, and then reconstructed by certain AR
to a residual image which is then weighted together with previous image iterate
to form next image iterate. Intuitively since the eigenvalues of AR-projection
operator are close to the unity, PFBS based AIR has a fast convergence. Such an
advantage is rigorously established through convergence analysis and numerical
computation of convergence rate. The proposed AIR method is validated in the
setting of circular cone-beam CT with AR being FDK and total-variation sparsity
regularization, and has improved image quality from both AR and IR. For
example, AIR has improved visual assessment and quantitative measurement in
terms of both contrast and resolution, and reduced axial and half-fan
artifacts.
