A differentiable Shepp–Logan phantom and its applications in exact cone-beam CT

Cone-beam composite-circling scan and exact image reconstruction for a quasi-short object

Here we propose a cone-beam composite-circling mode to solve the quasi-short object problem, which is to reconstruct a short portion of a long object from longitudinally truncated cone-beam data involving the short object. In contrast to the saddle curve cone-beam scanning, the proposed scanning mode requires that the X-ray focal spot undergoes a circular motion in a plane facing the short object, while the X-ray source is rotated in the gantry main plane. Because of the symmetry of the proposed mechanical rotations and the compatibility with the physiological conditions, this new mode has significant advantages over the saddle curve from perspectives of both engineering implementation and clinical applications. As a feasibility study, a backprojection filtration (BPF) algorithm is developed to reconstruct images from data collected along a composite-circling trajectory. The initial simulation results demonstrate the correctness of the proposed exact reconstruction method and the merits of the proposed mode.

A novel solid-angle tomosynthesis (SAT) scanning scheme

PURPOSE

Digital tomosynthesis (DTS) recently gained extensive research interests in both diagnostic and radiation therapy fields. Conventional DTS images are generated by scanning an x-ray source and flat-panel detector pair on opposite sides of an object, with the scanning trajectory on a one-dimensional curve. A novel tomosynthesis method named solid-angle tomosynthesis (SAT) is proposed, where the x-ray source scans on an arbitrary shaped two-dimensional surface.

METHODS

An iterative algorithm in the form of total variation regulated expectation maximization is developed for SAT image reconstruction. The feasibility and effectiveness of SAT is corroborated by computer simulation studies using three-dimensional (3D) numerical phantoms including a 3D Shepp-Logan phantom and a volumetric CT image set of a human breast.

RESULTS

SAT is able to cover more space in Fourier domain more uniformly than conventional DTS. Greater coverage and more isotropy in the frequency domain translate to fewer artifacts and more accurately restored features in the in-plane reconstruction.

CONCLUSIONS

Comparing with conventional DTS, SAT allows cone-shaped x-ray beams to project from more solid angles, thus provides more coverage in the spatial-frequency domain, resulting in better quality of reconstructed image.

Lambda tomography with discontinuous scanning trajectories

Lambda tomography (LT) is a well-known local reconstruction technology to reduce the radiation dose or accommodate a limited imaging geometry. After a theoretical analysis of the so-called Calderon operator (CO), the necessary conditions for exact LT reconstruction are presented in terms of the 2D and 3D COs. Based on our previous results on LT, a general scheme is proposed to construct exact LT formulae in terms of the 2D CO with multiple segment trajectories. Every 2D formula has a corresponding 3D cone-beam formula in the Feldkamp framework in terms of the 2D CO which was illustrated in a triple-segment case. Our simulation results verify the correctness and demonstrate the merits of the proposed scheme.

Approximate and exact cone-beam reconstruction with standard and non-standard spiral scanning

The long object problem is practically important and theoretically challenging. To solve the long object problem, spiral cone-beam CT was first proposed in 1991, and has been extensively studied since then. As a main feature of the next generation medical CT, spiral cone-beam CT has been greatly improved over the past several years, especially in terms of exact image reconstruction methods. Now, it is well established that volumetric images can be exactly and efficiently reconstructed from longitudinally truncated data collected along a rather general scanning trajectory. Here we present an overview of some key results in this area.

Practical cone-beam lambda tomography

As a potentially important technology for medical x-ray computed tomography (CT), lambda tomography (LT) is to reconstruct a gradient-like image only from local projection data. Based on our recently derived exact fan-beam LT formula, [H. Y. Gu and G. Wang, Int. J. Biomed. Imaging 2006(1), 1-9 (2006)] here we propose a practical cone-beam LT algorithm for LT reconstruction from local data collected along an arbitrary smooth three-dimensional curve. A key step in our algorithm is to determine an appropriate vector perpendicular to the line connecting the x-ray source and an image point. The algorithm is implemented assuming an equispatial planar detector and a nonstandard spiral trajectory. The numerical simulation results demonstrate the merits of our method.

Cone-beam mammo-computed tomography from data along two tilting arcs

Over the past several years there has been an increasing interest in cone-beam computed tomography (CT) for breast imaging. In this article, we propose a new scheme for theoretically exact cone-beam mammo-CT and develop a corresponding Katsevich-type reconstruction algorithm. In our scheme, cone-beam scans are performed along two tilting arcs to collect a sufficient amount of information for exact reconstruction. In our algorithm, cone-beam data are filtered in a shift-invariant fashion and then weighted backprojected into the three-dimensional space for the final reconstruction. Our approach has several desirable features, including tolerance of axial data truncation, efficiency in sequential/parallel implementation, and accuracy for quantitative analysis. We also demonstrate the system performance and clinical utility of the proposed technique in numerical simulations.

Data consistency based translational motion artifact reduction in fan-beam CT

A basic assumption in the classic computed tomography (CT) theory is that an object remains stationary in an entire scan. In biomedical CT/micro-CT, this assumption is often violated. To produce high-resolution images, such as for our recently proposed clinical micro-CT (CMCT) prototype, it is desirable to develop a precise motion estimation and image reconstruction scheme. In this paper, we first extend the Helgason-Ludwig consistency condition (HLCC) from parallel-beam to fan-beam geometry when an object is subject to a translation. Then, we propose a novel method to estimate the motion parameters only from sinograms based on the HLCC. To reconstruct the moving object, we formulate two generalized fan-beam reconstruction methods, which are in filtered backprojection and backprojection filtering formats, respectively. Furthermore, we present numerical simulation results to show that our approach is accurate and robust.