X-ray Image Reconstruction Using Direct Derivative Calculation
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Solution Overview
Problem
Current image reconstruction methods in computer tomography face challenges in achieving high spatial resolution due to interpolation errors during the calculation of derivatives and filtering processes, particularly when filtering lines are non-horizontal, leading to suboptimal image quality.
Innovation Solution
The method involves defining filtering lines for projection data filtering and determining sampling positions such that derivatives are calculated directly on these lines, eliminating the need for conventional interpolation and reducing resource intensity by only calculating derivatives at positions required for filtering.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional interpolation methods are used during derivative calculation and filtering, then the reconstruction process can handle non-horizontal filtering lines, but the spatial resolution and image quality deteriorate due to interpolation errors
Solution Approach 1:
The patent inverts the conventional approach by instead of interpolating projection data to calculate derivatives at arbitrary positions, it calculates derivatives directly at the original detector positions and then performs filtering. This inversion eliminates interpolation errors while maintaining the ability to handle non-horizontal filtering lines, thus resolving the contradiction between spatial resolution and process complexity
Solution Approach 2:
The patent extracts the interpolation step from the reconstruction process entirely. By calculating derivatives directly at measured positions and performing filtering separately, it removes the source of interpolation errors, thereby improving spatial resolution without significantly increasing overall process complexity
2Manufacturing precision
If derivatives are calculated at all detector positions and then interpolated to filtering line positions, then the filtering can be performed accurately, but the computational resources and processing time increase
Solution Approach 1:
The patent applies preliminary action by calculating derivatives directly at the original detector positions before filtering is performed. This preliminary calculation at measured positions eliminates the need for subsequent interpolation to filtering line positions, maintaining filtering accuracy while reducing computational overhead and improving processing efficiency
Solution Approach 2:
The patent performs partial action by calculating derivatives only at the necessary detector positions rather than at all possible positions. This selective calculation reduces the total number of derivative computations required while still providing sufficient data for accurate filtering, thereby improving processing efficiency without sacrificing filtering accuracy
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
This approach enhances the accuracy and efficiency of image reconstruction by directly calculating derivatives on filtering lines, improving image quality and reducing computational resources compared to conventional methods.
Implementation Method 1
x-ray radiation is transmitted through an object to be examined and is then recorded by a detector. The recording or projection represents an item of information about the attenuation of the transmitted x-rays on a path through the object. The attenuation of the x-ray radiation depends on the density of the parts of the object
Data Source
AI summary
A method for determining attenuation coefficients for an object using a movable x-ray source and a detector for recording projections is provided. The method includes defining a trajectory for the movable x-ray source, defining filtering lines for the filtering of projection data, and defining positions on the filtering lines, at which the projection derivative is to be formed using a mathematical algorithm for a back-projection. The method also includes defining sampling positions on the trajectory, traversing, by the x-ray source, the trajectory and recording a projection for each sampling position. Projection derivatives with respect to the trajectory path are calculated numerically for each of the positions directly on the filtering lines, and using a mathematical algorithm, attenuation coefficients are determined for the object from the calculated projection derivatives, for the reconstruction.