Generalized‐equiangular geometry CT: Concept and shift‐invariant FBP algorithms
Authors: Xia Yingxian , Zhang Li , Xing Yuxiang , Chen Zhiqiang , Gao Hewei 
Published: June 2023

Background

With advanced x‐ray source and detector technologies being continuously developed, non‐traditional CT geometries have been widely explored. Generalized‐Equiangular Geometry CT (GEGCT) architecture, in which an x‐ray source might be positioned radially far away from the focus of arced detector array that is equiangularly spaced, is of importance in many novel CT systems and designs.

Purpose

GEGCT, unfortunately, has no theoretically exact and shift‐invariant analytical image reconstruction algorithm in general. In this study, to obtain fast and accurate reconstruction from GEGCT and to promote its system design and optimization, an in‐depth investigation on a group of approximate Filtered Back‐Projection (FBP) algorithms with a variety of weighting strategies has been conducted.

Methods

The architecture of GEGCT is first presented and characterized by using a normalized‐radial‐offset distance (NROD). Next, shift‐invariant weighted FBP‐type algorithms are derived in a unified framework, with pre‐filtering, filtering, and post‐filtering weights, for both fixed and dynamic NROD configurations. Three viable weighting strategies are then presented including a classic one developed by Besson in the literature and two new ones generated from a curvature fitting and from an empirical formula, where all of the three weights can be expressed as certain functions of NROD. After that, an analysis of reconstruction accuracy is conducted with a wide range of NROD. Finally, the weighted FBP algorithm for GEGCT is extended to a three‐dimensional form in the case of cone‐beam scan with a cylindrical detector array.

Results

Theoretical analysis and numerical study show that weights in the shift‐invariant FBP algorithms can guarantee highly accurate reconstruction for GEGCT. A simulation of Shepp‐Logan phantom and a GEGCT scan of lung mimicked by using a clinical lung CT dataset both demonstrate that FBP reconstructions with Besson and polynomial weights can achieve excellent image quality, with Peak Signal to Noise Ratio and Structural Similarity being at the same level as that from the standard equiangular fan‐beam CT scan. Reconstruction of a cylinder object with multiple contrasts from simulated GEGCT scan with dynamic NROD is also highly consistent with fixed ones when using the Besson and polynomial weights, with root mean square error less than 7 hounsfield units, demonstrating the robustness and flexibility of the presented FBP algorithms. In terms of resolution, the direct FBP methods for GEGCT could achieve 1.35 lp/mm of spatial resolution at 10% modulation transfer functions point, higher than that of the rebinning method which can only reach 1.14 lp/mm. Moreover, 3D reconstructions of a disc phantom reveal that a greater value of NROD for GEGCT will bring less cone beam artifacts as expected.

Conclusions

We propose the concept of GEGCT and investigate the feasibility of using shift‐invariant weighted FBP‐type algorithms for reconstruction from GEGCT data without rebinning. A comprehensive analysis and phantom studies have been conducted to validate the effectiveness of proposed weighting strategies in a wide range of NROD for GEGCT with fixed and dynamic NROD.