Iterative CT Image Reconstruction Using Kalman Filter Approximations
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Solution Overview
Problem
Current tomography image reconstruction techniques, such as filtered back-projection (FBP) and iterative reconstruction (IR), face challenges with limited quantitative accuracy, inefficiency in using projections, and computational burdens due to large image element counts, especially in modern settings requiring 10^6 to 10^14 image elements.
Innovation Solution
A computer-implemented method using a combination of multi-grid computations, non-linear Kalman filter approximations, and efficient impulse response inversion to reconstruct images, allowing for arbitrary projection dimensions and directions, and adaptive gain adjustments to improve convergence and accuracy.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Speed
If filtered back-projection (FBP) is used for image reconstruction, then computation speed is improved, but quantitative accuracy deteriorates and projections are not used efficiently
Solution Approach 1:
The patent introduces an iterative refinement process as an intermediary step between FBP and final image reconstruction. The FBP provides an initial estimate, which then undergoes iterative correction using forward and back-projection operations. This intermediary iterative process improves quantitative accuracy while building upon the efficient FBP foundation.
Solution Approach 2:
The patent replaces the deterministic mechanical FBP process with a probabilistic iterative maximum likelihood estimation approach. Instead of directly computing the inverse Radon transform, the method uses iterative updates that model the statistical nature of projection data, substituting the mechanical inversion with a statistical optimization process that handles noise and inconsistencies more effectively.
2Reliability
If conventional iterative reconstruction techniques are used, then non-negative density estimates are ensured, but computational burden increases due to repeated inversion and forward projection operations
Solution Approach 1:
The patent applies preliminary non-negativity constraints during the iterative update process. Before each back-projection step, the update values are clipped to ensure non-negativity, preventing the computational burden of full matrix inversions while maintaining the reliability benefit of non-negative density estimates throughout the iteration process.
Solution Approach 2:
The patent applies different update rules to different regions of the image based on local characteristics. In regions where non-negativity is critical, constrained updates are applied, while in other regions, more efficient unconstrained updates are used. This local differentiation maintains reliability where needed while improving overall computational efficiency.
3Measurement precision
If matrix-based techniques are used for small problems, then exact solutions are obtained, but computational burden becomes unmanageable for typical tomographic reconstruction settings
Solution Approach 1:
The patent segments the large-scale reconstruction problem into smaller manageable components by processing the image in slices or regions. Instead of inverting one large matrix for the entire volume, the method breaks down the problem into multiple smaller matrix operations that can be handled efficiently, maintaining accuracy while reducing computational burden for large datasets.
Solution Approach 2:
The patent transforms the problem from direct matrix inversion in the spatial domain to an iterative optimization approach in the projection domain. By changing the dimensionality of the computational approach—from solving Ax=b directly to iteratively minimizing ||Ax-b||² with constraints—the method handles large-scale problems efficiently without sacrificing reconstruction accuracy.
4Measurement precision
If current optimization techniques are used for iterative reconstruction, then convergence is achieved, but improvement stalls beyond tens-to-hundreds of iterations due to Hessian matrix limitations
Solution Approach 1:
The patent dynamically changes optimization parameters during the iterative process. The update step size and constraint tightness are adjusted based on the iteration number and residual reduction rate. This parameter adaptation allows rapid initial convergence while preventing stalling in later iterations, reducing the total number of iterations needed to achieve high precision.
Solution Approach 2:
The patent introduces dynamic adaptation of the optimization process based on real-time feedback from the reconstruction progress. The algorithm monitors residual reduction and automatically adjusts the number and type of updates per iteration, transitioning from aggressive early updates to refined later updates. This dynamic approach maintains convergence momentum and prevents the stagnation that occurs with fixed-parameter methods.
Data Source
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AI summary
A system comprising: one or more transmitters to transmit an excitation energy into an object under observation; one or more detectors to generate projection space data encoding an energy received by the one or more detectors in response to the transmitted excitation energy into the object under observation; a controller to control the one or more transmitters to transmit the excitation energy and the one or more receivers to generate the projection space data; and an image reconstructor having at least one processor to receive the projection space data and to process the projection space data by: computing a first quantity characterizing a difference between the projection space data and predicted projection data, wherein the difference between the projection space data and predicted projection data is associated with a projection gain; recording, in a data storage device, a first data encoding the difference; computing a revised first quantity based on recorded first data from preceding iterations; computing an update value using the revised first quantity; and reconstructing an object space image representing the object under observation using the update value.