Hierarchical Tomography Reconstruction via Sparse Sampling
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Solution Overview
Problem
Current tomographic reconstruction methods, such as filtered backprojection, face computational bottlenecks, especially in high-resolution imaging and 3D reconstructions, requiring faster and more accurate techniques to handle increasing data volumes and complex geometries.
Innovation Solution
The method involves backprojecting selected projections to create intermediate images, applying digital image coordinate transformations and resampling to accurately represent these images with sparse samples, and aggregating them recursively to form pixel images, allowing for flexible trade-offs between accuracy and speed.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If filtered backprojection is used for tomographic reconstruction, then image quality is maintained, but computational requirements increase significantly
Solution Approach 1:
The patent divides the image reconstruction process into multiple resolution levels. Instead of processing the full-resolution image directly, the method performs backprojection at coarser resolutions first, then progressively refines the result at higher resolutions. This segmentation of the computational task across different scales reduces the overall computational burden while maintaining final image quality.
Solution Approach 2:
The patent introduces a hierarchical dimension to the traditional 2D backprojection process by adding the resolution level as an additional dimension. The reconstruction proceeds through multiple levels from coarse to fine resolution, transforming the single-step full-resolution backprojection into a multi-level process that reduces computational complexity.
2Measurement precision
If image resolution is increased from N to 2N, then image quality improves, but computational requirements increase by 8-fold
Solution Approach 1:
The patent segments the high-resolution reconstruction task into multiple lower-resolution steps. By performing backprojection at progressively higher resolutions rather than directly at the final high resolution, the method breaks down the computationally intensive task into manageable stages, each operating on smaller data sets.
Solution Approach 2:
The patent performs preliminary backprojection operations at coarser resolutions before proceeding to finer resolutions. This preliminary action at lower computational cost provides a foundation that guides and constrains the subsequent higher-resolution processing, reducing the overall computational burden of achieving high image resolution.
3Measurement precision
If full backprojection is performed for every projection, then reconstruction accuracy is maintained, but processing time increases
Solution Approach 1:
The patent segments the set of projections into groups that contribute to different resolution levels. Not all projections need to be fully backprojected at all resolution levels - some can be processed at coarser levels only. This segmentation allows the method to maintain reconstruction accuracy while reducing the total number of backprojection operations required.
Solution Approach 2:
The patent applies partial backprojection actions at different resolution levels. Instead of performing complete backprojection for all projections at full resolution, the method performs partial backprojection operations at intermediate resolutions, which is sufficient to maintain accuracy while reducing processing time.
Data Source
AI summary
Pixel images f are created from projections (q1 . . . qp) by backprojecting (100) selected projections to produce intermediate images (I1, m), and performing digital image coordinate transformations (102) and/or resampling (FIG. 31, 186, 192, 196) on selected intermediate images. The digital image coordinate transformations (102) are chosen to account for view angles of the constituent projections of the intermediate images and for their Fourier characteristics, so that the intermediate images may be accurately represented by sparse samples. The resulting intermediate images are aggregated into subsets (104), and this process is repeated in a recursive manner until sufficient projections and intermediate images have been processed and aggregated to form the pixel image f. Digital image coordinate transformation can include rotation (FIG. 18, 102), shearing (FIG. 10B, 120, 122), stretching, contractions (109), etc. Resampling can include up-sampling (101, 106), down-sampling (109), and the like. Projections (FIG. 32, pθ1 . . . pθ18) can be created from a pixel image (f), by performing digital image coordinate transformation (202) and/or resampling (204) and/or decimation (FIG. 32, 204; FIG. 33, 212) re-projecting the final intermediate image (208).