Tomographic Reconstruction via Parallel Gibbs Sampling
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Solution Overview
Problem
Gibbs sampling in Markov chain Monte Carlo methods for tomographic imaging is computationally intensive due to the high dimensionality of posterior probability density functions, making it impractical for high-resolution applications.
Innovation Solution
The method involves recognizing mutually independent points in the reconstruction grid and utilizing parallel processing to draw new random values in sets, where components are associated with these independent points, allowing for parallel computation without affecting each other's calculations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If Gibbs sampling is used for tomographic reconstruction, then image quality is improved, but computational time increases significantly
Solution Approach 1:
The reconstruction grid is divided into mutually independent points, allowing the Gibbs sampling process to be segmented into parallel tasks. Each independent point can be processed simultaneously without affecting others, resolving the contradiction between maintaining image quality through comprehensive sampling and reducing computational time through parallelization.
Solution Approach 2:
The patent introduces a temporal dimension to parallel processing by drawing new random values in sets across multiple time steps. This dimensional approach enables simultaneous computation at different grid points while maintaining the sequential integrity of the Markov chain, thereby reducing computational time without sacrificing image quality.
2Productivity
If parallel processing is implemented, then computational efficiency is improved, but system complexity increases
Solution Approach 1:
The system complexity is managed by segmenting the reconstruction grid into mutually independent points, which allows parallel processing without requiring complex coordination between all grid points. This segmentation enables simplified parallel implementation where each point can be processed independently, improving productivity while keeping system complexity manageable.
Solution Approach 2:
Each mutually independent point in the grid serves itself by drawing new random values independently without requiring coordination or communication with other points. This self-service approach improves computational efficiency through parallelization while avoiding the complexity of inter-point coordination and synchronization.
3Measurement precision
If high-resolution reconstruction is performed, then image detail is improved, but computational intensity increases
Solution Approach 1:
The high-resolution reconstruction grid is segmented into mutually independent points, enabling parallel processing that distributes computational intensity across multiple processors or cores. This segmentation allows high-resolution image detail to be achieved without excessive computational intensity concentrated on a single processor, as the workload is divided into independent tasks.
Solution Approach 2:
The patent resolves the computational intensity problem by adding a parallel dimension to the reconstruction process. High-resolution image detail is maintained through comprehensive sampling, while computational intensity is reduced by distributing the sampling across multiple time steps and processors, effectively moving the computational burden from a single intensive task to multiple lighter concurrent tasks.
Data Source
AI summary
A method is provided for constructing a tomographic reconstruction through the application of statistical inversion. Unknowns associated with points of a reconstruction grid are represented with components of a vector-valued variable. A next version of the vector-valued variable is repeatedly created by drawing for each component a value from a conditional distribution. The components of a so generated version of the vector-valued variable are used as the tomographic reconstruction. The components are divided into sets, so that components in a set represent unknowns associated with mutually independent points of the reconstruction grid, or into independent collections. For at least two components of a set or at least two collections, the drawing of values from a conditional distribution is performed in parallel in a computer-implemented process.