Separable Quadratic Surrogate PET Image Reconstruction
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Solution Overview
Problem
Current statistical image reconstruction algorithms for positron emission tomography (PET) are computationally intensive and slow, requiring substantial time to converge, which hinders the achievement of improved image quality at reduced radiation doses and increased computational efficiency.
Innovation Solution
The use of a novel separable quadratic surrogate function in combination with Nesterov acceleration and ordered subsets methods for iterative reconstruction, allowing for precomputation of certain components and reducing computational complexity by using only one forward-projection and one back-projection per iteration, while accelerating convergence using a combination of these methods.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If statistical image reconstruction algorithms are used to improve image quality at reduced radiation doses, then image quality is improved, but computational time increases substantially
Solution Approach 1:
The patent divides the computational workload into ordered subsets, processing different portions of the data in each iteration. This segmentation allows the algorithm to make progress on multiple data elements simultaneously, reducing the total number of iterations needed while maintaining the statistical reconstruction quality benefits.
Solution Approach 2:
The patent performs precomputation of system matrices and other computational components before the main reconstruction process. By preparing these elements in advance, the iterative statistical reconstruction algorithm requires less computational time during the actual reconstruction iterations, thereby reducing overall computational time while preserving image quality improvements.
2Productivity
If conventional reconstruction methods like filtered back-projection are used, then computational speed is maintained, but image quality deteriorates at reduced radiation doses
Solution Approach 1:
The patent employs dynamic iterative algorithms that adapt the reconstruction process based on the specific characteristics of the acquired data. Unlike static conventional methods, these dynamic algorithms can adjust their behavior during reconstruction to optimize both speed and quality, achieving faster convergence than traditional statistical methods while maintaining superior image quality at reduced doses.
Solution Approach 2:
The patent modifies key algorithmic parameters such as regularization strength, subset size, and iteration criteria to optimize the balance between computational speed and image quality. By dynamically adjusting these parameters during reconstruction, the method achieves faster convergence while preserving the quality benefits of statistical reconstruction at reduced radiation doses.
3Manufacturing precision
If iterative statistical reconstruction algorithms are used to achieve improved image quality, then manufacturing precision is improved, but device complexity increases
Solution Approach 1:
The patent segments the complex statistical reconstruction algorithm into modular ordered subsets, each handling specific data elements. This modular approach simplifies the implementation of the overall algorithm by breaking down the complexity into manageable, independent computational units that can be processed systematically.
Solution Approach 2:
The patent introduces intermediate computational structures such as precomputed system matrices and surrogate objective functions that mediate between the raw acquisition data and the final reconstructed image. These intermediaries simplify the computational pathway, reducing the apparent complexity of the statistical reconstruction algorithm while maintaining its ability to produce high-quality images.
Data Source
AI summary
A method and apparatus is provided to iteratively reconstruct a PET image for emission data using separable quadratic surrogates (SQS). The quadratic surrogates include a Poisson likelihood surrogate that has a curvature that depends on a back-projection of an inverse of mean-background signal. The method can be used with Nesterov acceleration and ordered subsets to achieve quadratic convergence to an image minimizing a Poisson Likelihood objective function that includes a regularizer that penalizes roughness in the reconstructed image.