CT Image Reconstruction Acceleration via Ordered Subsets and Conjugate Gradient
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Solution Overview
Problem
Iterative reconstruction (IR) methods in computed tomography (CT) face challenges with slow convergence rates, leading to high computational costs and long reconstruction times, despite offering improved image quality at reduced doses. Existing acceleration techniques like Nesterov's acceleration and ordered subsets (OS) can introduce issues such as inexact gradients and limit cycles, limiting their effectiveness.
Innovation Solution
The combination of conjugate-gradient (CG) methods with ordered subsets (OS) and restarting mechanisms addresses the convergence issues by using OS accelerated CG-based IR, which includes resetting parameters and employing preconditioners to achieve global convergence and reduce computational burden.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If statistical iterative reconstruction (IR) algorithms are used, then image quality is improved, but computational time increases substantially
Solution Approach 1:
The patent divides the complete set of measurement data into multiple ordered subsets, processing each subset separately in successive iterations. This segmentation allows the algorithm to make progress through partial updates rather than requiring complete data processing in each iteration, significantly reducing computational time while maintaining image quality.
Solution Approach 2:
The patent implements periodic restarting of the conjugate gradient process at predetermined intervals or when convergence criteria are met. This periodic action prevents the algorithm from entering limit cycles and ensures continued convergence, reducing the total number of iterations needed while preserving reconstruction accuracy.
2Speed
If Nesterov's acceleration method is used, then convergence speed is improved, but inexact gradients and limit cycles occur
Solution Approach 1:
The patent periodically restarts the conjugate gradient process to prevent the algorithm from entering limit cycles. This periodic intervention maintains convergence stability by resetting the search direction when necessary, eliminating the reliability issues associated with continuous acceleration methods.
Solution Approach 2:
The patent monitors convergence criteria and uses this feedback to determine when to restart the conjugate gradient process. This feedback mechanism ensures that acceleration is applied effectively while preventing the development of inexact gradients and limit cycles, maintaining both speed and reliability.
3Productivity
If ordered subsets (OS) method is used, then computational cost is reduced, but limit cycles and convergence issues arise
Solution Approach 1:
The patent implements periodic restarting of the conjugate gradient process when using ordered subsets. This periodic action interrupts the development of limit cycles that can occur with OS methods, ensuring reliable convergence while preserving the computational efficiency benefits of subset processing.
Solution Approach 2:
The patent merges the ordered subsets method with the conjugate gradient algorithm and periodic restarting strategy. This combination integrates the computational efficiency of OS with the convergence reliability of CG and periodic restarts, achieving both high productivity and reliable convergence behavior.
4Measurement precision
If more iterations are performed, then image quality improves, but reconstruction time increases
Solution Approach 1:
The patent segments measurement data into ordered subsets, allowing the reconstruction to progress through multiple passes over different subsets rather than requiring many iterations over complete data sets. This achieves image quality improvement with fewer apparent iterations, reducing reconstruction time.
Solution Approach 2:
The patent uses periodic restarting with convergence criteria to determine when sufficient image quality has been achieved. This prevents unnecessary continued iterations once adequate reconstruction is obtained, optimizing the balance between image quality and reconstruction time.
Data Source
AI summary
A method and apparatus is provided to reconstruct a computed tomography image using iterative reconstruction (IR) that is accelerated using various combinations of ordered subsets, conjugate gradient, preconditioning, resetting/restarting, and/or gradient approximation techniques. For example, when restarting criteria are satisfied the IR algorithm can be reset by setting conjugate-gradient parameters to initial values and/or by changing the number of ordered subsets. The IR algorithm can be accelerated by approximately calculating the gradients, by using a diagonal or Fourier preconditioner, and by selectively updating the preconditioner based on the regularization function. The update direction and step size can be calculated using the preconditioner and a surrogate function, which is not necessarily separable.