Iterative Image Reconstruction Using Hessian Inversion
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Solution Overview
Problem
Iterative reconstruction algorithms in CT imaging require significantly more computational effort than direct reconstruction techniques, leading to slower image generation due to multiple iterations and computationally intensive projection and back-projection operations, despite offering improved image quality and reduced X-ray dosage.
Innovation Solution
The method involves iteratively updating image element subsets by directly inverting or approximating the Hessian matrix, with termination based on a completion criterion, and enforcing non-negativity to restrict updates within specified ranges, allowing for parallel processing and accelerated convergence.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If iterative reconstruction algorithms are used to improve image quality and reduce X-ray dosage, then image quality is improved and radiation dose is reduced, but computational time increases significantly
Solution Approach 1:
The patent divides the image into multiple blocks or regions and processes them independently through iterative reconstruction. This segmentation allows parallel computation across different image regions, significantly reducing total computational time while maintaining the quality improvements from iterative algorithms. Each block can be reconstructed using the full iterative method, and results are combined to form the final image.
Solution Approach 2:
The patent introduces a spatial dimension by organizing image pixels into blocks that can be processed in parallel. This transforms a sequential one-dimensional processing approach into a multi-dimensional parallel architecture, enabling simultaneous computation across multiple image regions and reducing overall reconstruction time.
2Reliability
If multiple iterations with projection and back-projection operations are performed, then image quality improves and artifacts are reduced, but computational effort increases by an order of magnitude
Solution Approach 1:
By segmenting the image into blocks, the patent reduces the computational complexity of each individual iteration. Instead of processing the entire image matrix in each projection and back-projection operation, only smaller block matrices are processed, reducing the order of magnitude computational effort per iteration while maintaining the reliability improvements through multiple iterations.
Solution Approach 2:
The patent applies iterative reconstruction to only the necessary portions of the image (blocks) rather than the entire image simultaneously. This partial action approach reduces the computational burden per iteration while still achieving convergence to the correct solution through multiple iterations across different blocks.
Data Source
AI summary
Methods are provided for iteratively reconstructing an image signal to generate a reconstructed image signal. In one embodiment, sub-iterations of each iteration are performed on pixel or voxel subsets. The subsets may be composed of neighboring or spatially separated pixel or voxels and may extend in the z-direction. In one embodiment, an update step of the iterative reconstruction involves the direct inversion of an approximation of a Hessian matrix associated with the respective subsets. In further embodiments, non-negativity or other limitations or constraints on update values may be enforced.