X-Ray Tomographic Reconstruction With Pixel Uncertainty Mapping
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Solution Overview
Problem
Conventional X-ray tomographic reconstruction methods fail to provide accurate uncertainty maps due to neglecting pixel correlations, leading to suppressed details and inadequate defect detection in industrial parts or medical diagnostics.
Innovation Solution
An iterative reconstruction method that generates a plurality of reconstructions using a kernel function to ensure proper distribution and diversity, followed by calculating an average reconstruction with associated uncertainty indicators.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If conventional filtered back-projection methods are used for X-ray tomographic reconstruction, then the reconstruction process is fast and simple, but reconstruction artefacts occur due to non-linear phenomena, photon counting uncertainties, and electronic noise
Solution Approach 1:
The patent transforms the reconstruction problem from a deterministic parameter estimation into a statistical inference problem by introducing probability distributions over the object's attenuation coefficients. This allows the method to account for uncertainties in the projection data while maintaining computational feasibility through variational inference and normalizing flows, resolving the contradiction between speed and accuracy by using probabilistic modeling rather than more complex iterative methods.
Solution Approach 2:
The patent introduces normalizing flows as an intermediary transformation that maps a simple prior distribution into a complex posterior distribution over the object's attenuation coefficients. This intermediary structure enables the method to capture correlations between pixels and model uncertainty without requiring direct computation of the intractable posterior, thus achieving accurate reconstructions with uncertainty quantification while avoiding the computational burden of traditional iterative methods.
2Device complexity
If an uncertainty map is estimated using conventional methods, then the computational cost is reduced by neglecting pixel correlations, but details in the reconstruction are suppressed and defect detection is inadequate
Solution Approach 1:
The patent uses normalizing flows as an intermediary that transforms a simple isotropic prior distribution into a complex anisotropic posterior distribution that captures pixel correlations. This intermediary transformation allows the method to model uncertainties with full correlation structure without directly computing the complex posterior covariance matrix, thus achieving accurate uncertainty maps with proper detail preservation while maintaining computational efficiency through the flow-based approach.
Solution Approach 2:
The patent changes the parameterization of the uncertainty model from direct covariance estimation to transformation-based uncertainty propagation. By using normalizing flows to transform random samples through the learned mapping, the method automatically captures correlation structures in the uncertainty without requiring explicit covariance computation, resolving the contradiction between computational complexity and uncertainty estimation accuracy.
3Reliability
If iterative reconstruction methods with a priori models are used, then reconstruction artefacts are compensated, but the methods still only provide an estimate of the object interior without accurate uncertainty information
Solution Approach 1:
The patent transitions from static deterministic reconstruction to dynamic probabilistic inference by introducing normalizing flows that learn a transformation from prior to posterior distributions. This dynamic approach allows the method to not only produce accurate reconstructions but also to track and quantify uncertainties throughout the reconstruction process, capturing the full distribution of possible solutions rather than a single point estimate.
Solution Approach 2:
The patent introduces normalizing flows as an intermediary that bridges the gap between the simple prior distribution and the complex posterior distribution. This intermediary structure enables the method to maintain accurate reconstruction quality while simultaneously preserving uncertainty information, as the flow transformation explicitly models the evolution from prior to posterior and allows for uncertainty propagation through the learned mapping.
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
Provides realistic and diverse reconstructions with accurate uncertainty maps, enhancing defect detection and diagnosis by ensuring proper distribution and evaluating pixel/voxel uncertainty.
Implementation Method 1
the attenuation of the X-rays inside the object depends on the energy of the source
Data Source
AI summary
An x-ray tomographic method for reconstructing an object, includes, on the basis of a plurality of images, each image in the plurality of images corresponding to a projection of the object, reconstructing the object using an iterative reconstruction method so as to produce a plurality of reconstructions x(m) of the object.