Tomographic Image Reconstruction via Angular Offset Sampling
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Conventional Algebraic Reconstruction Techniques (ARTs) for tomographic imaging require extensive computational resources and time due to large-scale calculations, making it impractical to obtain high-quality, high-definition images, especially for three-dimensional volume imaging, as they involve huge numbers of simultaneous linear equations with insufficient equations compared to variables, leading to iterative approximation challenges.
Innovation Solution
A method employing an unconventional sampling technique with an appropriate offset angle for the discrete inverse Radon transform, which allows for the reconstruction of high-definition images using a smaller computational resource by ensuring the system matrix has an inverse matrix, thereby overcoming the limitations of conventional ARTs.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional ARTs are used for tomographic image reconstruction, then image quality can be improved, but computational resources and time required become excessively large
Solution Approach 1:
The patent applies parameter changes by introducing an offset angle to the detection direction arrangement. Specifically, the detection directions are arranged such that at least one detection direction is offset from the coordinate axes by a predetermined angle. This angular parameter modification transforms the system matrix properties, enabling it to become regular (non-singular) and thus invertible, which directly reduces computational complexity and reconstruction time while maintaining image quality
2Manufacturing precision
If conventional ARTs are used for high-definition image reconstruction, then image definition can be improved, but the calculation scale becomes huge requiring large computational resources
Solution Approach 1:
The patent modifies the angular parameter of the detection system by introducing an offset angle. This parameter change ensures that the system matrix becomes regular even for high-definition images with large numbers of pixels, making the matrix invertible and avoiding the need for complex iterative solutions, thereby reducing computational resource requirements while achieving high image definition
3Measurement precision
If conventional ARTs are used for three-dimensional volume imaging, then image quality can be improved, but the number of simultaneous linear equations becomes huge with insufficient equations compared to variables
Solution Approach 1:
The patent applies parameter changes to the angular configuration of detection directions. By offsetting at least one detection direction from the coordinate axes by a predetermined angle, the system matrix for three-dimensional volume imaging becomes regular and invertible. This transforms an underdetermined system with insufficient equations into a determinate system that can be solved directly, dramatically reducing system complexity for 3D reconstruction
Data Source
AI summary
In an embodiment of the present disclosure, in order to raise the reproducibility of a reconstructed tomographic image without increasing a calculation load, any one among two directions adjacent to two boundaries that demarcate an angular scan range is offset from any one among coordinate axes of a two-dimensional tomographic image of N pixels×N pixels, and the angle of the offset is made to be above 0 degrees and under 90 degrees or above −90 degrees and under 0 degrees. A detection device, which includes N detection elements, performs detection in each detection direction, and a first vector having N×N elements is obtained from a detection signal obtained by the detection device in a detection operation. A discrete Inverse Radon transform matrix is applied to the first vector to obtain a second vector having N×N elements. The second vector is de-vectorized to obtain image data for a two-dimensional tomographic image of N pixels×N pixels. An inverse matrix of a system matrix for an offset is obtained and used as the discrete Inverse Radon transform matrix.