Tomographic Reconstruction Algorithm for X-Ray Cone-Beam Scan Data
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Current algorithms for reconstructing cone-beam x-ray scan data in tomographic imaging, such as the FDK algorithm, suffer from severe artifacts in short scan scenarios, particularly in C-arm CT applications, and are not optimal for data without extrapolation, especially outside the central plane.
Innovation Solution
A novel tomographic reconstruction algorithm using shift-invariant filtering and backprojection with a 1D Hilbert transform is proposed, which combines conventional FDK reconstruction with differential backprojection to suppress artifacts, allowing for optimal reconstruction on a short scan comparable to a full scan, even with reduced data acquisition.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If FDK algorithm is used for short scan reconstruction, then computation efficiency is improved through 1D shift-invariant filtering, but severe cone-beam artifacts are introduced
Solution Approach 1:
The patent applies the Hilbert transform to convert the harmful cone-beam artifacts into beneficial correction terms. The Hilbert transform of the FDK reconstruction produces a correction image that, when subtracted from the original FDK reconstruction, eliminates the artifacts while preserving the computational efficiency of the 1D shift-invariant filtering structure.
Solution Approach 2:
The patent introduces an intermediary correction term based on the Hilbert transform between the FDK reconstruction and the final result. This intermediary correction image acts as a mediator that removes the harmful artifacts without requiring a complete redesign of the reconstruction algorithm, thus maintaining computational efficiency while eliminating cone-beam artifacts.
2Quantity of substance
If Parker's weighting modification is applied to FDK, then data redundancy is handled, but reconstruction accuracy is limited to mid-plane only
Solution Approach 1:
The patent extends the correction approach from the mid-plane (2D) to the entire 3D volume by applying the Hilbert transform in the third dimension (z-direction). This dimensional extension allows the correction to be applied uniformly across all slices, achieving accurate reconstruction throughout the entire volume rather than just the mid-plane.
3Loss of time
If short scan data acquisition is used, then examination time is reduced, but reconstruction quality deteriorates compared to full scan
Solution Approach 1:
The patent performs preliminary action by pre-calculating the Hilbert transform correction term from the FDK reconstruction. This preliminary correction calculation allows the short scan reconstruction to achieve full-scan quality by applying the correction after the initial FDK reconstruction, thus compensating for the reduced data acquisition without requiring additional scan time.
4Manufacturing precision
If mathematical exact algorithm is applied to short scan, then data redundancy is handled exactly, but reconstruction optimality is not achieved
Solution Approach 1:
The patent changes the parameter of the reconstruction algorithm by introducing the Hilbert transform operation. This parameter change transforms the reconstruction from a mathematically exact but non-optimal solution to an optimal solution that achieves both exact data redundancy handling and optimal reconstruction quality, as demonstrated by the elimination of cone-beam artifacts and improvement in image quality metrics.
Data Source
AI summary
Disclosed is x-ray cone beam scan data reconstruction of an imaged object with a reconstruction algorithm using shift invariant filtering and backprojection with the maximum tomographic capability of a circular scan larger than p plus cone angle, when CB data is not truncated and data extrapolation is not allowed. The reconstruction scheme includes a conventional FDK reconstruction and a parallel reconstruction using differential back projection and 1D Hilbert transform to suppress the CB artifacts.