Iterative Algorithms for Variance Reduction in Compressed PET Sinograms
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Solution Overview
Problem
Existing methods for estimating random coincidences in PET imaging are not directly applicable to compressed data, leading to inefficiencies in data processing and reconstruction due to the need for complex algorithms and resource-intensive computations.
Innovation Solution
Development of simple update iterative algorithms, including a monotonic sequential coordinate descent algorithm and simultaneous update algorithms, which optimize the Least Squares and Poisson Likelihood functions to estimate singles rates from compressed data, allowing for easy adaptation to any acquisition geometry and parallelization.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If existing methods for estimating random coincidences are used on compressed data, then measurement precision may be maintained, but device complexity and computational resources increase significantly
Solution Approach 1:
The patent transforms the estimation problem by changing the parameter space - instead of directly estimating random coincidences from compressed data, it estimates singles rates first, then derives random coincidences from them. This parameter transformation simplifies the mathematical formulation and enables efficient iterative algorithms that work directly with compressed data without requiring decompression or complex preprocessing.
Solution Approach 2:
The patent divides the estimation process into separate iterative update steps for different parameters (singles rates for different detector elements). Each iteration updates one parameter while holding others fixed, breaking down the complex joint estimation problem into simpler sequential sub-problems that are computationally tractable and can be efficiently implemented.
2Measurement precision
If complex algorithms are used to estimate random coincidences from compressed data, then measurement precision may be maintained, but productivity decreases due to resource-intensive computations
Solution Approach 1:
The patent employs dynamic iterative algorithms that adaptively update parameter estimates based on current data and previous estimates. The iterative nature allows the computation to converge to accurate solutions while enabling early termination when sufficient precision is achieved, balancing computational resources with measurement precision requirements in a dynamic manner.
Solution Approach 2:
The patent uses simplified mathematical models and approximations that replicate the essential statistical properties of random coincidences without requiring full simulation or complex calculations. By working with compressed data directly through simplified update rules, it achieves accurate estimates with significantly reduced computational overhead compared to methods that require full data reconstruction or complex Monte Carlo simulations.
3Loss of substance
If compressed data formats are used to reduce data storage, then loss of substance is reduced, but difficulty of detecting and measuring increases
Solution Approach 1:
The patent performs preliminary statistical modeling and formulation of estimation algorithms specifically tailored for compressed data structures. By pre-developing update rules and estimation procedures that work directly with compressed representations, it eliminates the need for data decompression or complex transformation steps, making the measurement process straightforward despite the compressed format.
Solution Approach 2:
The patent introduces singles rate estimates as intermediate parameters that bridge the gap between compressed data and random coincidence estimates. These intermediaries serve as mathematical mediators that allow accurate estimation to proceed directly from compressed data without requiring intermediate decompression or complex detection procedures, thus reducing both storage requirements and measurement difficulty.
Data Source
AI summary
The use of the ordinary Poisson iterative reconstruction algorithm in PET requires the estimation of expected random coincidences. In a clinical environment, random coincidences are often acquired with a delayed coincidence technique, and expected randoms are estimated through variance reduction (VR) of measured delayed coincidences. In this paper we present iterative VR algorithms for random compressed sonograms, when previously known methods are not applicable. Iterative methods have the advantage of easy adaptation to any acquisition geometry and of allowing the estimation of singles rates at the crystal level when the number of crystals is relatively small. Two types of sonogram compression are considered: axial (span) rebinning and transaxial mashing. A monotonic sequential coordinate descent algorithm, which optimizes the Least Squares objective function, is investigated. A simultaneous update algorithm, which possesses the advantage of easy parallelization, is also derived for both cases of the Least Squares and Poisson Likelihood objective function.