Spectral CT Material Decomposition Using Patch Probability Maps
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Solution Overview
Problem
Existing material decomposition methods in spectral imaging, such as dual energy CT, struggle to accurately decompose materials beyond three, as it is an ill-posed deterministic problem.
Innovation Solution
A computer system employing a statistical module that fits probability distributions to spectral imagery patches, using Gaussian mixture models, to generate localized probability maps for material types, allowing decomposition into four or more materials by combining these distributions adaptively.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If deterministic material decomposition methods are used for spectral imaging, then decomposition into two or three materials can be achieved, but decomposition into more than three materials becomes an ill-posed problem
Solution Approach 1:
The patent transforms the deterministic decomposition problem into a statistical framework by changing the mathematical parameters from fixed linear equations to probability distributions. This allows the system to handle ill-posed problems by incorporating statistical variability and uncertainty, enabling decomposition into more than three materials while maintaining accuracy through probabilistic modeling rather than deterministic constraints.
Solution Approach 2:
The patent introduces probability distributions as an intermediary between the spectral data and material decomposition results. Instead of directly solving the ill-posed deterministic system, the method uses statistical models to mediate the decomposition process, allowing robust handling of materials beyond three by incorporating prior knowledge and uncertainty quantification through probabilistic frameworks.
2Measurement precision
If linear system of equations is used for material decomposition, then two material decomposition can be achieved accurately, but the method cannot discriminate between more than three materials
Solution Approach 1:
The patent moves the decomposition problem from a deterministic algebraic dimension to a statistical probability dimension. By formulating material decomposition in terms of probability distributions and statistical models rather than fixed linear equations, the method gains an additional dimensional framework that can accommodate more material types while maintaining mathematical tractability and accuracy.
3Loss of information
If spectral imaging is used for material decomposition, then material specific image data segmentation is enabled, but decomposition into more than three materials is an ill-posed problem
Solution Approach 1:
The patent incorporates feedback mechanisms through iterative statistical optimization and model fitting. The probabilistic framework allows the system to continuously refine material decomposition estimates by comparing predicted spectral signatures with actual measurements and adjusting probability distributions accordingly, thereby improving reliability for multi-material decomposition while preserving detailed material composition information.
Data Source
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AI summary
A computer system (MD) and relates method for spectral-data based material decomposition. The system comprises a statistical module (SM) configured to fit, per patch in input spectral imagery, a set of probability distributions (Pk) to a respective vector spectral diagram (5) for the respective patch (A). The patch is one of a plurality of patches in the input spectral imagery obtained by operation of a spectral imaging apparatus. The probability distributions are combinable into a probability map indicative of material type probabilities per image location in the input spectral imagery.