Interior Tomography Reconstruction Using Invertible Wavelet Transforms
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Conventional x-ray computed tomography (CT) systems face challenges in achieving unique and precise interior reconstruction due to non-uniqueness of solutions from limited data, and existing methods like compressive sensing require invertible sparsifying transforms which the discrete gradient transform does not satisfy, limiting their applicability in interior tomography.
Innovation Solution
The implementation of a sparsity-based interior tomography method using invertible sparsifying transforms like wavelet transforms and pseudo-inverse transforms, allowing for exact and numerically reliable reconstruction of interior regions of interest (ROI) from truncated local projections, enabling ultrafast temporal resolution with reduced radiation dose.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional CT reconstruction methods are used with limited projection data, then the reconstruction process is simple, but the solution is non-unique and reconstruction precision deteriorates
Solution Approach 1:
The patent changes the parameter of sparsity representation by transforming the image into different domains (wavelet, gradient, finite difference) where the image becomes sparse. This allows exact reconstruction from limited data by exploiting the sparsity property, resolving the non-uniqueness issue while maintaining computational feasibility through L1-norm minimization.
Solution Approach 2:
The patent introduces an additional dimension by considering the transform domain alongside the spatial domain. By formulating the reconstruction problem in terms of sparse coefficients in a transform domain, the method adds a new dimension to the solution space, enabling unique reconstruction from limited projections.
2Object-affected harmful factors
If compressive sensing with discrete gradient transform is used, then radiation dose is reduced, but the transform is non-invertible and reconstruction reliability deteriorates
Solution Approach 1:
The patent changes the parameter of invertibility by selecting transform operators that are invertible (wavelet transform, finite difference transform with pseudo-inverse) rather than using the non-invertible discrete gradient transform. This ensures that the sparsity representation can be reliably converted back to the image domain, maintaining reconstruction reliability while still achieving dose reduction through compressive sensing.
3Measurement precision
If more projection data is collected to improve reconstruction uniqueness, then reconstruction precision improves, but scanning time and temporal resolution worsen
Solution Approach 1:
The patent applies partial action by collecting only the necessary minimum number of projections required for accurate interior reconstruction, rather than acquiring complete 360-degree data. By using compressive sensing with sparsity constraints, the method achieves exact reconstruction from a subset of projection data, significantly reducing scanning time while maintaining precision for interior regions of interest.
4Measurement precision
If complete projection data is acquired for unique solution, then reconstruction precision improves, but radiation dose increases
Solution Approach 1:
The patent changes the parameter of data completeness by demonstrating that complete projection data is not necessary for unique reconstruction when sparsity constraints are applied. By formulating the problem in a sparse transform domain and using L1-norm minimization, the method achieves exact reconstruction from truncated, limited-angle, or few-view projection data, thereby reducing radiation dose while maintaining precision.
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 enables faithful resolution of features inside the ROI using limited data, providing ultrafast imaging with improved temporal resolution and reduced radiation dose, enhancing imaging performance and efficiency in CT systems.
Implementation Method 1
The implementation of a sparsity-based interior tomography method using invertible sparsifying transforms like wavelet transforms
Implementation Method 2
Conventional x-ray computed tomography (CT) systems face challenges in achieving unique and precise interior reconstruction
Data Source
AI summary
A system and method for tomographic image reconstruction using truncated projection data that allows exact interior reconstruction (interior tomography) of a region of interest (ROI) based on the known sparsity models of the ROI, thereby improving image quality while reducing radiation dosage. In addition, the method includes parallel interior tomography using multiple sources beamed at multiple angles through an ROI and that enables higher temporal resolution.