Tomographic Image Reconstruction via Oversampling and Decimation
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Solution Overview
Problem
Conventional Algebraic Reconstruction Techniques (ARTs) for tomographic imaging require significant computational resources and time due to large-scale calculations, especially when increasing the number of imaging pixels, leading to impractical processing times for acquiring high-quality tomographic images.
Innovation Solution
A method employing unconventional sampling combined with appropriate processing for the discrete inverse Radon transform, involving oversampling and decimation to reduce the number of equations, allowing for a more efficient algebraic solution, thereby generating high-definition images with reduced computational resources.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If conventional ARTs are used to increase the number of imaging pixels, then image quality is improved, but computational resources and processing time increase significantly
Solution Approach 1:
The patent changes the sampling parameters by using non-uniform sampling intervals in the projection domain. Instead of conventional uniform sampling, the invention applies variable sampling densities across different angular ranges, transforming the problem into an algebraic system that can be solved more efficiently while maintaining image quality
Solution Approach 2:
The patent replaces the conventional iterative mechanical reconstruction process with an algebraic solution method. By formulating the reconstruction problem as a system of linear equations with variable sampling, it eliminates the need for repeated iterative calculations while achieving the same image quality, thus improving processing speed
2Manufacturing precision
If conventional ARTs are used to increase the number of imaging pixels, then manufacturing precision is improved, but device complexity increases
Solution Approach 1:
The patent modifies the sampling parameters to create a non-uniform distribution of measurement points. This parameter change transforms the reconstruction problem into an algebraic system with variable coefficients, which can be solved with reduced computational complexity while maintaining high image quality
Solution Approach 2:
The patent segments the projection data into different angular ranges with different sampling densities. By dividing the measurement space and applying appropriate sampling strategies to each segment, it simplifies the overall computational problem while preserving image quality
3Manufacturing precision
If iterative reconstruction is performed 100 times or more to reduce noise and artifacts, then image quality is improved, but loss of time increases
Solution Approach 1:
The patent replaces the time-consuming iterative reconstruction process with a direct algebraic solution method. By formulating and solving the reconstruction problem as a system of linear equations with variable sampling, it achieves noise reduction and artifact elimination in a single calculation step rather than through hundreds of iterations
Solution Approach 2:
The patent performs preliminary sampling design and algebraic system formulation before reconstruction. By carefully designing the variable sampling scheme in advance, it prepares the problem structure to enable direct solution without requiring subsequent iterative refinements, thus saving time
Data Source
AI summary
In order to increase reproducibility of a reconstructed tomographic image without increasing the computational load, detection is performed by oversampling in (N+n) directions during imaging for detection by N detection elements. A vector having N×(N+n) elements is obtained, and vector decimation step is performed in which a total of n×N elements corresponding to a sequence {k} 30 denoting a decimation order are removed. In a discrete Radon transform step, a corresponding discrete Radon inverse matrix WSQ−140 is operated, and in an image data generation step, de-vectoring is performed, thereby tomographic image data are acquired. When oversampling is used, a discrete Radon inverse matrix WSQ−1 is obtained. Therefore, a tomographic image is obtained by matrix computation without resorting to iterative approximation.