Optimization-based algorithms for image reconstruction in multi-spectral (or photon-counting) computed tomography (MCT) remains a topic of active research. The challenge of optimization-based image reconstruction in MCT stems from the inherently non-linear data model that can lead to a non-convex optimization program for which no mathematically exact solver seems to exist for achieving globally optimal solutions. In the work, based upon a non-linear data model, we design a non-convex optimization program, derive its first-order-optimality conditions, and propose an algorithm to solve the program for image reconstruction in MCT. In addition to consideration of image reconstruction for standard scan configuration, an emphasis of the work is on investigating the algorithm’s potential for enabling non-standard scan configurations with no or minimum hardware modification to existing CT systems, which can be of potential practical implications for lowered hardware cost, enhanced scanning flexibility, and reduced imaging dose/time in MCT. Numerical studies are carried out for verification of the algorithm and its implementation, and for a preliminary demonstration and characterization of the algorithm in reconstructing images and in enabling non-standard configurations with varying scanning angular range and/or X-ray illumination coverage in MCT.

A circular scanning trajectory is and will likely remain a popular choice of trajectory in computed tomography (CT) imaging because it is easy to implement and control. Filtered-backprojection (FBP)-based algorithms have been developed previously for approximate and exact reconstruction of the entire image or a region of interest within the image in circular cone-beam and fan-beam cases. Recently, we have developed a 3D FBP-based algorithm for image reconstruction on PI-line segments in a helical cone-beam scan. In this work, we demonstrated that the 3D FBP-based algorithm indeed provided a rather general formulation for image reconstruction from divergent projections (such as cone-beam and fan-beam projections). On the basis of this formulation we derived new approximate or exact algorithms for image reconstruction in circular cone-beam or fan-beam scans, which can be interpreted as special cases of the helical scan. Existing algorithms corresponding to the derived algorithms were identified. We also performed a preliminary numerical study to verify our theoretical results in each of the cases. The results in the work can readily be generalized to other non-circular trajectories.

Algorithms have been developed for image reconstruction within a region-of-interest (ROI) from fan-beam data less than that required for reconstructing the entire image. However, these algorithms do not admit truncated data. In this work, we investigate exact ROI-image reconstruction from fan-beam data containing truncations by use of the so-called fan-beam backprojection-filtration (BPF) algorithm. We also generalize the fan-beam BPF algorithm to exploit redundant information inherent in the truncated fan-beam data. Because the parallel-beam scan can be interpreted as a special case of the fan-beam scan, based upon the fan-beam BPF algorithm, we derive a parallel-beam BPF algorithm for exactly reconstructing ROI images from truncated parallel-beam data. Furthermore, we investigate image reconstruction within two types of distinctive ROIs, which are referred to as the peripheral and central ROIs, respectively, from fan-beam data containing truncations and discuss their potential clinical applications. The results can readily be generalized to reconstructing 3D ROI images from data acquired in circular and helical cone-beam scan. They can also be extended to address ROI-image-reconstruction problems in parallel-, fan-, and cone-beam scans with general trajectories. The work not only has significant implications for clinical and animal-imaging applications of CT, but also may find applications in other imaging modalities.

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We investigate an optimization-based reconstruction, with an emphasis on image-artifact reduction, from data collected in C-arm cone-beam computed tomography (CBCT) employed in image-guided interventional procedures. In the study, an image to be reconstructed is formulated as a solution to a convex optimization program in which a weighted data divergence is minimized subject to a constraint on the image total variation (TV); a data-derivative fidelity is introduced in the program specifically for effectively suppressing dominant, low-frequency data artifact caused by, e.g., data truncation; and the Chambolle-Pock (CP) algorithm is tailored to reconstruct an image through solving the program. Like any other reconstructions, the optimization-based reconstruction considered depends upon numerous parameters. We elucidate the parameters, illustrate their determination, and demonstrate their impact on the reconstruction. The optimization-based reconstruction, when applied to data collected from swine and patient subjects, yields images with visibly reduced artifacts in contrast to the reference reconstruction, and it also appears to exhibit a high degree of robustness against distinctively different anatomies of imaged subjects and scanning conditions of clinical significance. Knowledge and insights gained in the study may be exploited for aiding in the design of practical reconstructions of truly clinical-application utility.