arXiv subjects

Jiayu Duan

Publications and source records attributed to Jiayu Duan.

3 recordsLinked to original sources

arXiv2026

Geometry-Consistent Discretization of Local Correlation Equations for the Radon Transform in Clinical CT

In this work, we extend the local correlation equation (LCE) framework of the 2D Radon transform to clinical computed tomography (CT) geometry and propose a set of geometry-consistent discretization schemes. Building upon the dual-center-of-rotation formulation, the 1st and 2nd LCEs are reformulated under circular fan-beam geometry and discretized using finite difference methods aligned with clinical acquisition configurations. The numerical validity of the proposed discretized circular LCEs (cLCEs) is evaluated using projection data generated from clinical CT datasets. Quantitative analysis based on residual error, mean absolute error (MAE), and mean percentage error (MPE) demonstrates strong consistency between both sides of the equations, with the 2nd cLCE exhibiting the highest accuracy. Furthermore, the proposed cLCE framework is applied to sparse-view sinogram interpolation. By refining interpolated projections using a gradient-descent-based scheme without additional regularization, improved reconstruction quality is achieved. Experimental results show that the cLCE-refined projections significantly enhance image quality compared to sparse-view reconstruction and can outperform clinical complete view (CCV) reconstruction under certain conditions. These results demonstrate that the proposed cLCE discretization provides an effective tool for exploiting projection redundancy in clinical CT and has strong potential for sparse-view reconstruction applications.

physics.med-ph↗

arXiv2025

A CT Geometry With Multiple Centers Of Rotation For Solving Sparse View Problem

With the emergence of CNT (Carbon nanotube), static and instant CT scanning becomes possible. By transforming the traditionally rotated thermal source into a static ring array source composed of multiple CNTs, the imaging system can achieve high temporal resolution in scanning. However, due to the non-negligible packaging size of CNTs, the static CT based on CNTs faces sparse view problem, which affects the image quality by introducing streak artifacts. In this study, we based on the local correlation equation (LCE) to address the sparse view problem of static CT. The LCE is a series of partial differential equations (PDEs) to describe the local correlation of Radon transform in a neighborhood projection domain. Based on LCE, we analyze the characteristic of sparse view projection and propose a scanning geometry with multiple rotation centers, which is different from existing CT devices that acquires the projection around one rotation center. Specifically, in the proposed scanning geometry, the circular ring array X-ray sources is divided into several arcs while the sources of each arc share one rotation center. All rotation centers of the arcs are uniformly distributed on a small circle. The optimal distribution of the rotation centers can be optimized by the radius of the circle. Moreover, to elevate the image quality under the sparse view reconstruction, we employed the LCE to interpolate unmeasured projections. Compared to the single rotation center scheme used in existing CT geometries, the multiple rotation centers scan contributes to a more even projection distribution with same view number. The simulated results demonstrated the efficiency and potential applications of the proposed method in static CT reconstructions.

physics.med-ph↗

arXiv2024

Exploring the redundancy of Radon transform using a set of partial derivative equations: Could we precisely reconstruct the image from a sparse-view projection without any image prior?

In this study, we proposed a universal n-th order partial differential equation (PDE) of 2-D Radon transform to disclose the relationship of Radon transform over a neighborhood of the integral line, named as local correlation equation (LCE). It is independent to the imaging object while in present CT theory, the relationship of Radon transform over neighboring integral line had been described depended on the imaging objection. Hence, the LCE is the first PDE to reveal the universal correlation property of Radon transform. The LCE can be applied to either of 2D CT projections or any 2-D profile of 3-D CT projections. The correlation also provides the redundancy property of Radon transform. In this regard, we carried out a preliminary study on sparse-view CT reconstruction by using a discrete first order LCE to interpolate missing projections in sparse-view sampling without knowing image prior. Meanwhile, we also proposed a unified reconstruction framework that combines a regularized iterative reconstruction with the LCE based interpolation method to handle the sparse-view CT problem with higher sparsity level. The conducted experiments have credibly validated the proposed LCE, projection interpolation method, and the unified reconstruction scheme. The result of this study suggests an attractive possibility that a sparse-view projection may contain enough information of the complete projection, by which projection completeness in CT scanning may not be necessity. This possibility would bring profound changes in CT geometry designs and reconstruction algorithms. Moreover, this study initiates an appealing research topic of exploring the redundancy property of Radon transform and investigating new CT theories based on the redundancy property, which will boost the further development of CT reconstructions.

physics.med-ph↗