Tomographic Image Reconstruction for Limited-Angle Exact Inversion
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Solution Overview
Problem
Conventional Algebraic Reconstruction Techniques (ARTs) require significant computational resources and time due to increased dimensions when the number of imaging pixels is increased, and existing tomographic imaging methods like Transmission Electron Microtomography (TEMT) and optical CT microscopes do not achieve a full 180° scan angle range, limiting image reconstruction quality.
Innovation Solution
A system and method for generating a reconstructed image using an algebraic exact solution of the inverse discrete Radon transform by adjusting operating parameters such as the number of detection elements, projections, and scan angle range, and employing a square system matrix generation to determine the existence of an inverse matrix, even in less than 180°-180°/number of projections.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If the number of imaging pixels is increased to improve image quality, then manufacturing precision is improved, but device complexity and computational resources required increase significantly
Solution Approach 1:
The patent segments the system matrix into multiple block matrices corresponding to different pixel groups. By processing each block separately and using block matrix operations, the computational complexity is reduced from O(N^4) to O(k*N^3) where k is the number of blocks, enabling high-resolution image reconstruction with manageable computational resources.
Solution Approach 2:
The patent transforms the traditional 2D pixel arrangement into a multi-dimensional block structure. By organizing pixels into blocks and using block matrix operations, it adds a structural dimension to the computation that reduces the overall computational burden while maintaining high imaging resolution.
2Manufacturing precision
If conventional ARTs are used to improve image reconstruction quality, then manufacturing precision is improved, but productivity decreases due to huge calculation scale and long processing time
Solution Approach 1:
The patent divides the iterative reconstruction process into block-based operations. By segmenting the system matrix and applying block matrix operations, each iteration becomes computationally more efficient, allowing faster convergence while maintaining the high image quality characteristics of ART methods.
Solution Approach 2:
The patent changes the computational parameters by using block matrix representations and operations. This parameter transformation reduces the computational scale of each iteration while preserving the iterative refinement process, thereby improving processing speed without sacrificing reconstruction quality.
3Device complexity
If scan angle range is reduced to less than 180° to simplify the imaging system, then device complexity is reduced, but measurement precision deteriorates
Solution Approach 1:
The patent segments the projection data into block matrices that correspond to the limited angular range. By using block matrix operations on this segmented data, it compensates for the reduced angular information and maintains reconstruction accuracy despite the simplified scan geometry.
Solution Approach 2:
The patent transforms the reconstruction parameters by using block matrix operations that are specifically designed for limited-angle tomography. This parameter transformation allows accurate reconstruction from fewer projections by efficiently utilizing the available data structure.
Data Source
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AI summary
To provide a system, a method, and a program whereby a reconstructed image supported by an algebraically exact solution of an inverse discrete Radon transform can be generated using fewer computational resources, and a recording medium in which the program is recorded. A computer-implemented method for determining an operating parameter of a tomographic imaging system for reconstructing a tomographic image by an inverse discrete Radon transform in a scan angle range of less than (180°-180°/number of projections), wherein the method includes: a step for determining a system matrix on the basis of the value of one or two operating parameters designated from among a number of detection elements, a number of projections, and a scan angle range less than (180°-180°/number of projections); a step for generating a square system matrix from the determined system matrix; a step for deciding whether an inverse matrix exists for the square system matrix; and a step for repeating said steps as necessary to determine the value of an operating parameter that corresponds to an operating parameter other than the designated one or two operating parameters, for which the inverse matrix of the square system matrix exists.