Area-Simulating-Volume Algorithm for 3D PET Reconstruction
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Solution Overview
Problem
Current methods for calculating geometric probabilities in PET reconstruction are inefficient, leading to artifacts and long computation times, especially in 3D PET reconstruction, where accurate and fast algorithms are required for quantitative imaging.
Innovation Solution
The area-simulating-volume (ASV) algorithm calculates geometric probabilities by determining distance ratios in multiple planes and multiplying them to estimate the intersected volume between a voxel and a tube-of-response, using an adaptive common plane and selective edge projections to minimize errors and improve accuracy.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional methods are used to calculate geometric probabilities in PET reconstruction, then measurement precision is maintained, but productivity is significantly reduced due to long computation times
Solution Approach 1:
The patent segments the 3D volume calculation into multiple 2D plane calculations. Specifically, it divides the voxel-TOR intersection volume computation into calculating intersection areas in different planes (e.g., axial, coronal, sagittal planes) and then combines these 2D results to obtain the 3D geometric probability. This segmentation reduces computational complexity while maintaining accuracy.
Solution Approach 2:
The patent uses 2D intersection area calculations as copies or projections of the 3D intersection volume problem. By calculating the intersection areas in 2D planes and using these as surrogate measurements, the method avoids the computationally intensive direct 3D volume calculation while preserving the essential geometric relationships needed for accurate geometric probability determination.
2Manufacturing precision
If traditional 3D methods are used to calculate intersected volume, then manufacturing precision is improved, but loss of time increases significantly
Solution Approach 1:
The patent transforms the 3D volume calculation problem into a series of 2D area calculation problems by projecting the voxel and tube-of-response intersections onto different planes. The geometric probability is then derived from these 2D intersection areas rather than directly computing the 3D intersected volume, significantly reducing computational time while maintaining precision.
3Productivity
If fast approximation algorithms are used, then productivity is improved, but measurement precision deteriorates due to artifacts
Solution Approach 1:
The patent replaces the mechanically intensive direct 3D volume integration method with a mathematical substitution approach using 2D plane projections and area calculations. This substitution maintains measurement precision by preserving the geometric relationships through mathematical equivalence while dramatically improving computation speed.
Data Source
AI summary
A method, device, and system for calculating first and second distance ratios used to calculate a geometric probability between a voxel and a tube-of-response (TOR). The method includes determining a first-edge-line including a first-middle-point, determining a second-edge-line including a second-middle-point, determining a middle line of the TOR, projecting a first point of a first surface of the voxel to the middle line, projecting a second point of a second surface of the voxel to the middle line, calculating a first distance between one of the first and second middle-points and the first-projected-point, and a second distance between the one of the first and second middle-points and the second-projected-point, and determining a first distance ratio based on the first and second distances. The method calculates the second distance ratio similarly to the first distance ratio. The geometric probability is proportional to the product of the first and second distance ratios.