PET Sinogram Interpolation via Direct Triangulation

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Solution Overview

Problem

In PET imaging, interpolating a raw LOR sinogram is challenging due to difficulty in determining nearest neighbors for non-rectangular grid sampling points and the lack of a systematic method to handle irregularly distributed sampling points, with linear triangular interpolation being non-trivial and sensitive to unit variations.

Innovation Solution

A direct triangulation method is used to connect adjacent sampling points row-by-row, forming triangles that maximize the minimal angle, and barycentric interpolation is performed to generate a uniformly sampled sinogram, simplifying the triangulation process and improving interpolation results.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Adaptability or versatility

If linear triangular interpolation method is used for scattered sampling points, then interpolation can be performed on non-rectangular grids, but the method becomes complex and sensitive to unit variations

Engineering Contradiction:

Improveinterpolation capability for scattered sampling pointsVSAvoidinterpolation method complexity

Core Design Contradiction:

Adaptability or versatilityVSDevice complexity

Solution Approach 1:

The patent transforms the coordinate system from physical units to normalized indices by introducing transformation equations that map scattered sampling points to a regular grid structure. This parameter change eliminates sensitivity to unit variations and simplifies the interpolation process while maintaining adaptability for scattered sampling points.

Inventive Principle:

Principle #35Parameter changes

Solution Approach 2:

The patent introduces an intermediate coordinate transformation step that acts as a mediator between the scattered sampling points and the interpolation process. By transforming coordinates to a normalized index system before interpolation, the method simplifies the overall process and reduces complexity while preserving the ability to handle scattered data.

Inventive Principle:

Principle #24Intermediary (Mediator)

2Measurement precision

If Delaunay triangulation is used to form triangles from scattered sampling points, then optimal triangulation is achieved, but the method is computationally intensive and complex to implement

Engineering Contradiction:

Improvetriangulation optimalityVSAvoidtriangulation implementation complexity

Core Design Contradiction:

Measurement precisionVSDevice complexity

Solution Approach 1:

The patent changes the parameter representation from physical coordinates requiring Delaunay triangulation to normalized index coordinates where triangles can be directly formed by connecting adjacent points. This parameter transformation maintains triangulation quality while dramatically simplifying implementation and reducing computational complexity.

Inventive Principle:

Principle #35Parameter changes

Solution Approach 2:

The patent segments the triangulation process into simple sequential steps of connecting adjacent sampling points in the normalized index space, replacing the complex global Delaunay triangulation algorithm with local, straightforward triangle formation that is easier to implement and compute.

Inventive Principle:

Principle #1Segmentation

3Adaptability or versatility

If irregularly distributed sampling points are processed using conventional interpolation, then scattered data can be handled, but systematic method is lacking and nearest neighbor determination is difficult

Engineering Contradiction:

Improvehandling of irregular sampling distributionVSAvoidnearest neighbor determination ease

Core Design Contradiction:

Adaptability or versatilityVSEase of operation

Solution Approach 1:

The patent transforms the coordinate system from physical space with irregular sampling distribution to a normalized index space where sampling points can be systematically accessed. This parameter change enables easy determination of nearest neighbors through simple index comparison while maintaining the ability to handle irregularly distributed data.

Inventive Principle:

Principle #35Parameter changes

Solution Approach 2:

The patent creates a universal coordinate transformation framework that works for any scattered sampling point distribution. The normalized index system provides a systematic method that universally handles irregular distributions while simplifying nearest neighbor determination through index-based ordering.

Inventive Principle:

Principle #6Universality (Multi-functionality)

Data Source

PatentEP2629117B1Pet data processing method, pet data processing device, computer-readable recording medium, and data processing method

Publication Date: 2019.10.23 TOSHIBA MEDICAL SYST CORP

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AI summary

A PET data processing method, a PET data processing apparatus, a computer-readable storage medium, and a data processing method which are capable of generating a uniformly sampled sinogram are provided. A method of interpolating positron emission tomography (PET) data for reconstructing a PET image, includes acquiring (201) PET event data, which was obtained by scanning an object using a PET scanner; generating (202) a two-dimensional line-of-response (LOR) sinogram from the acquired PET event data; determining (203) a plurality of triangles connecting sampling points within the LOR sinogram, wherein adjacent sampling points are connected horizontally row-by-row within the LOR sinogram to determine the plurality of triangles; and determining (208) a uniformly sampled sinogram from the LOR sinogram using the determined plurality of triangles.