Multi-basis-image reconstruction from conventional data acquired in standard CT.

Objective.We investigate and develop an algorithm to invert the well-established non-linear data model in standard computed tomography (CT) for numerically accurate and stable reconstruction of multi (⩾2)-basis images directly from a set of conventional data collected with a single spectrum in standard CT.Approach.Using the basis-region technique to reduce the number of voxel values, i.e. unknowns, in the basis images to be reconstructed and the volume-conservation constraint to augment conventional data, we formulate the reconstruction problem (i.e. the inverse problem) as a non-convex optimization program and develop the dynamic non-convex primal-dual (dNCPD) algorithm to empirically solve the optimization program for numerically accurate and stable reconstruction of multi-basis images from conventional data.Main results.We conduct studies to verify numerically the reconstruction accuracy of the dNCPD algorithm with simulated conventional data and also studies to evaluate the stability of the dNCPD algorithm with real conventional data that contain noise and other physical factors. The study results reveal that the dNCPD algorithm can numerically accurately and stably yield multi-basis images and virtual monochromatic images from conventional data.Significance.The work can be of theoretic interest and practical implication as it reveals the possibility of yielding multi-basis images from conventional data in standard CT, instead of data collected in dual-energy, multi-spectra, or photon-counting CT.