Variance-Reduced CT Image Reconstruction Algorithm
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Iterative reconstruction (IR) methods in computed tomography face slow convergence rates due to variance issues when combining ordered subsets (OS) with Nesterov's acceleration, leading to potential divergence and limit cycles, which prolong reconstruction time without ensuring image quality.
Innovation Solution
A variance-reduced method is introduced, using a surrogate for the gradient approximation to reduce noise accumulation, allowing for faster convergence by computing a full gradient and applying it to correct subset gradients, thereby maintaining optimal convergence rates without additional parameters.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Speed
If ordered subsets (OS) with Nesterov's acceleration are used to speed up iterative reconstruction, then convergence speed is improved, but variance accumulation causes divergence and limit cycles
Solution Approach 1:
The patent introduces a variance reduction term as an intermediary component that mediates between the accelerated gradient updates and the objective function minimization. This term acts as a stabilizing mechanism that prevents divergence while preserving the acceleration benefits, resolving the contradiction between speed and reliability.
Solution Approach 2:
The patent modifies the update rule by introducing a variance reduction parameter that dynamically adjusts the gradient update behavior. By changing the parameter structure to include variance reduction terms, the algorithm maintains fast convergence while preventing the variance accumulation that leads to divergence.
2Measurement precision
If standard statistical iterative reconstruction is used to ensure image quality, then accuracy is improved, but computation time increases substantially
Solution Approach 1:
The patent performs preliminary variance reduction calculations during the iterative process, preparing correction terms in advance that prevent noise accumulation. This preliminary action allows the algorithm to maintain high accuracy without requiring excessive computation time, as the variance reduction terms are computed efficiently alongside the main reconstruction steps.
Solution Approach 2:
The patent segments the computation into ordered subsets, processing different portions of the data in parallel while applying variance reduction to each subset. This segmentation enables faster computation by utilizing parallel processing, while the variance reduction terms ensure that accuracy is maintained despite the divided computation approach.
3Measurement precision
If more iterations are performed to reduce noise, then image quality is improved, but reconstruction time increases
Solution Approach 1:
The patent replaces the mechanical approach of simply increasing iteration count with a more efficient mechanism that uses variance reduction terms. Instead of relying on prolonged iteration to reduce noise, the algorithm actively reduces variance through corrected gradient updates, achieving better image quality in fewer iterations and thus reducing reconstruction time.
Data Source
AI summary
A method and apparatus is provided to reconstruct a computed tomography image using iterative reconstruction combined with variance-reduced acceleration techniques. The acceleration techniques including: ordered subsets, separable quadratic surrogates, and Nesterov's acceleration. Ordered subset iteration is used, but instead of calculating a gradient of the objective function for only one subset per iteration, a full gradient of the total objective function is used. This decreases the variance and mitigates limit cycles. A correction term is calculated as the difference between the subset gradient and the full gradient, and this correction term is used when performing the update of the reconstructed image. The ordered subset can be combined with Nesterov's acceleration. To improve computational efficiency, the full gradient can be calculated once every T iterations, with negligible degradation to the convergence rate.