Hybrid Fourier-Real Space Tomographic Reconstruction
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Solution Overview
Problem
Traditional tomographic imaging techniques face significant computational burdens due to large data sets generated by high-resolution detector arrays and sources, leading to impractically long reconstruction times and memory issues, especially when using real-space weight matrices and Algebraic Reconstruction Techniques.
Innovation Solution
A hybrid approach that selects subsets of large tomographic datasets in frequency space while maintaining others in real space, allowing for fast computational times and accurate reconstruction by inverting the weight matrix to obtain tomographic representations in real space.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If large detector arrays and sources are used to increase measurement precision, then image quality and spatial resolution are improved, but computational time and memory requirements increase significantly
Solution Approach 1:
The patent segments the large weight matrix into smaller blocks corresponding to different detector arrays and source positions. By processing these blocks separately and combining results, the system maintains image quality from large detector arrays while reducing computational burden through divide-and-conquer processing.
Solution Approach 2:
The patent transforms the reconstruction problem from real space to Fourier space, adding a frequency domain dimension to the processing. This transformation enables more efficient computation by exploiting the convolution theorem and reducing the complexity of matrix operations while preserving spatial resolution information.
2Measurement precision
If real-space weight matrices are used with Algebraic Reconstruction Techniques, then quantitative accuracy is improved, but memory requirements and computational complexity increase
Solution Approach 1:
The patent performs the inversion operation in Fourier space rather than real space. By transforming the weight matrix and measurement data to the frequency domain, the system exploits the diagonal structure of Fourier-space operators to reduce computational complexity while maintaining quantitative accuracy through proper inverse transformation.
Solution Approach 2:
The patent changes the representation parameters of the weight matrix from real-space coordinates to Fourier-space frequencies. This parameter transformation reveals underlying structures in the data that can be exploited for more efficient computation, reducing both memory requirements and operational complexity.
3Productivity
If complete Fourier approaches are used to reduce measurements, then computational efficiency is improved, but reconstruction artifacts increase
Solution Approach 1:
The patent applies different processing strategies to different regions of the frequency spectrum. Low-frequency components are processed using Fourier-space inversion for efficiency, while high-frequency components are handled with techniques that preserve spatial accuracy, thereby reducing artifacts while maintaining computational advantages.
Solution Approach 2:
The patent creates a composite reconstruction approach that combines elements of both real-space and Fourier-space methods. By integrating the strengths of both approaches—using Fourier transformation for efficient low-frequency processing and real-space techniques for high-frequency detail—the system achieves both computational efficiency and high reconstruction quality.
Data Source
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AI summary
The invention relates to systems and methods for tomographic imaging in diffuse media employing a fast reconstruction technique. A hybrid Fourier approach is presented that enables the fast tomographic reconstruction of large datasets. In certain embodiments, the invention features methods of in vivo fluorescence molecular tomographic (FMT) reconstruction of signals, reporters and/or agents (i.e., contrast agents or probes) in a diffusive medium (e.g., a mammalian subject). The method preserves the three-dimensional fluorophore distribution and quantitative nature of the FMT approach while substantially accelerating its computation speed, allowing FMT imaging of larger anatomies.