A linear shift-variant model for local point response in circular-orbit cone-beam iterative reconstruction

The authors develop and evaluate a spatial-domain model of the local point response arising from iterative reconstruction of circular-orbit cone-beam projections. They proceed from the premise that the missing data in circular-orbit cone-beam is spatially variant. They model the process of circular-orbit cone-beam projection and reconstruction as a linear, shift-variant process, implying that each point in the image space has a different point spread function (PSF). To estimate the local PSF of a given point, the authors determine the surface on which a simple backprojected point response would occur for any point source in the image space. Taking the Fourier transform of this function gives an expression for the missing data region of the Fourier space. For points on the axis of rotation, this space is described by a right circular cone. For points off the axis of rotation, the space is described by a skewed elliptical cone. The authors confirm the model by simulating circular-orbit cone-beam data for individual point sources and reconstructing with an iterative algorithm. Fourier transforms of the estimated point responses show that iterative reconstruction exhibits missing data regions similar to those predicted by the model; however, the authors conclude that further refinements would be required to make the model practical for use in an optimal shift-variant restoration procedure.