CT Reconstruction Denominator Stabilization
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Solution Overview
Problem
Conventional iterative CT reconstruction methods using the separable paraboloid surrogate (SPS) method with ordered subsets face instability and artifacts due to inaccurate denominator calculations, especially in spectral CT applications with multiple materials, leading to divergent reconstructions and reduced convergence speed.
Innovation Solution
The method employs an ordered subset maximum likelihood optimization with a diagonal paraboloid approximation and calculates a pre-computable block-diagonal denominator term for spectral CT, using variance or generalized-mean of diagonal terms to stabilize the algorithm and reduce computational complexity, allowing for monotonic convergence even with nonzero background events.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Speed
If conventional SPS method with ordered subsets is used for iterative CT reconstruction, then convergence speed is improved, but reconstruction stability deteriorates due to inaccurate denominator calculations
Solution Approach 1:
The patent pre-calculates the denominator terms using all available projection data before the iterative reconstruction process begins. This preliminary calculation ensures that the denominator values are accurate and consistent throughout the iterative process, preventing the instability that arises from recalculating denominators during iterations with ordered subsets.
Solution Approach 2:
The patent modifies the conventional SPS approach by changing how the denominator parameter is handled. Instead of calculating denominators separately for each subset during iterations, the method uses a unified pre-calculated denominator that accounts for all subsets, thereby maintaining parameter consistency and reconstruction stability while preserving fast convergence.
2Device complexity
If diagonal Hessian approximation is used in SPS method, then computational complexity is reduced, but accuracy deteriorates especially in spectral CT with multiple materials
Solution Approach 1:
The patent segments the Hessian matrix approximation by material type in spectral CT. Instead of using a single diagonal approximation for all materials, the method calculates separate diagonal Hessian approximations for each material component (e.g., bone, soft tissue, contrast agent), allowing accurate representation of material-specific properties while maintaining computational efficiency through the diagonal structure.
Solution Approach 2:
The patent applies different diagonal Hessian approximation qualities to different regions and materials. By calculating material-specific diagonal terms that reflect local statistical properties of each material type, the method achieves high local accuracy in heterogeneous spectral CT data while preserving the overall computational simplicity of the diagonal approximation approach.
3Productivity
If ordered subsets are used for cost function optimization, then iteration speed is improved, but solution exactness deteriorates leading to artifacts
Solution Approach 1:
The patent performs preliminary calculation of the denominator using the complete set of projection data before applying ordered subsets for optimization. This ensures that the exact solution components are captured in the denominator, while the ordered subsets are then used only for efficient gradient-based updates, thereby maintaining solution exactness while achieving fast iteration speed.
Solution Approach 2:
The patent applies ordered subsets partially - using them for the gradient calculation in each iteration but combining this with a pre-calculated denominator that represents the full dataset. This partial application of ordered subsets achieves speed improvement without the full negative impact on solution exactness that would occur if ordered subsets were used for the complete optimization.
Data Source
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AI summary
The present invention relates to a device for reconstructing an X-ray tomography image, the device comprising a reconstruction module, which is configured to utilize an ordered subset maximum likelihood optimization with a diagonal paraboloid approximation of a cost function for the reconstructing of the X-ray tomography image; and a calculation module, which is configured to calculate a pre-computable denominator term for the cost function for a plurality of subsets of projection data based on a distribution of diagonal denominator terms over the plurality of the subsets of the projection data.