PET Reconstruction Using MLEM with Latent Variables
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Solution Overview
Problem
Current PET image reconstruction methods discard a significant number of coincidences, particularly those involving tissue scattered photons, and require additional radiation exposure and dedicated equipment for obtaining the photon attenuation map, which is not feasible in combined PET/MRI scanners.
Innovation Solution
A method using the Maximum Likelihood Expectation Maximization (MLEM) algorithm with latent random variables to reconstruct intra-patient tissue activity distribution and photon attenuation map, incorporating Time of Flight data and Single Scatter Approximation, and accounting for detector scatter by setting a low energy threshold or incorporating scatter events into the MLEM method.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If transmission scan is used to obtain photon attenuation map, then attenuation map accuracy is improved, but patient radiation exposure increases and scan time is prolonged
Solution Approach 1:
The patent recovers and utilizes scattered coincidences that were previously discarded in conventional PET reconstruction. By incorporating these scattered photons into the reconstruction algorithm through the MLEM method with scatter modeling, the system obtains attenuation information without requiring additional transmission scans, thus avoiding extra radiation exposure while maintaining attenuation map accuracy
Solution Approach 2:
The system uses the PET emission data itself to generate the attenuation map through iterative reconstruction algorithms that model scatter and attenuation processes. This self-service approach eliminates the need for separate transmission scans, reducing patient radiation exposure while providing accurate attenuation correction
2Measurement precision
If transmission scan is used to obtain photon attenuation map, then attenuation map accuracy is improved, but overall scan time is prolonged
Solution Approach 1:
The patent merges the attenuation map acquisition process with the emission data reconstruction process. By combining scatter correction and attenuation correction into a single iterative MLEM reconstruction framework, the system obtains both activity distribution and attenuation map simultaneously from emission data, eliminating the need for separate transmission scans and reducing total scan time
Solution Approach 2:
The iterative MLEM reconstruction continuously utilizes all available coincidence data (including scattered coincidences) to progressively refine both activity and attenuation estimates. This continuous utilization of data throughout the reconstruction process eliminates idle time associated with separate transmission scans while maintaining accuracy
3Measurement precision
If true coincidences only are used for reconstruction, then reconstruction accuracy is improved, but number of usable coincidences decreases
Solution Approach 1:
The patent converts harmful scattered coincidences into beneficial data sources. By modeling the scatter process and incorporating scattered coincidences into the MLEM reconstruction algorithm, the system transforms previously harmful events into useful information for both activity distribution and attenuation map reconstruction, increasing the number of usable coincidences while maintaining accuracy
Solution Approach 2:
The patent changes the reconstruction parameters by introducing scatter modeling capabilities and using a probabilistic approach to distinguish true and scattered coincidences. This allows the system to utilize a broader range of coincidence events with appropriate weighting, increasing the effective number of usable coincidences while preserving reconstruction accuracy
4Quantity of substance
If scattered coincidences are incorporated into reconstruction, then number of usable coincidences increases, but computational complexity increases
Solution Approach 1:
The patent segments the reconstruction process into distinct components: scatter modeling, attenuation correction, and activity reconstruction. By separating these functions and using iterative MLEM updates that process different coincidence types through structured forward and back-projection operations, the system manages computational complexity while incorporating scattered coincidences
Solution Approach 2:
The patent implements partial scatter correction by modeling only the dominant scatter processes (single scatter approximation) rather than all possible scatter events. This partial approach captures the most significant scatter effects while limiting computational complexity, allowing incorporation of scattered coincidences without excessive computational burden
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
This approach increases the number of useful coincidences, results in a separable likelihood function for easier maximization, and allows for parallel reconstruction with a modest increase in computational complexity, effectively addressing measurement errors and incorporating a priori information from MRI data.
Implementation Method 1
the numbers of photon pairs emitted from an electron-positron annihilation inside a voxel that arrive into two given voxels along a Line of Response (LOR)
Implementation Method 2
incorporating Time of Flight (TOF) data
Implementation Method 3
incorporating a priori information from MRI data
Implementation Method 4
tissue scattered coincidences where only one of the two photons is scattered and is scattered only once
Data Source
AI summary
A method of PET image reconstruction is provided that includes obtaining intra-patient tissue activity distribution and photon attenuation map data using a PET/MRI scanner, and implementing a Maximum Likelihood Expectation Maximization (MLEM) method in conjunction with a specific set of latent random variables, using an appropriately programmed computer and graphics processing unit, wherein the set of latent random variables comprises the numbers of photon pairs emitted from an electron-positron annihilation inside a voxel that arrive into two given voxels along a Line of Response (LOR), where the set of latent random variables results in a separable joint emission activity and a photon attenuation distribution likelihood function.