Oblique Ray Interpolation for 3D Nuclear Image Reconstruction
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Solution Overview
Problem
Current methods for reconstructing tomographic images from projection data, such as back-projection and filtered back-projection, suffer from blurring and inadequate noise reduction, with algorithms like regularized maximum likelihood being computationally expensive and producing biased images, while existing projection calculation methods like the Square Pixel Method and forward projection method have limitations in clarity and processing time.
Innovation Solution
A method involving interpolating oblique rays through a rectangular volume by projecting them onto a surface, matching with direct rays, shearing the volume, and interpolating within the sheared space to improve image clarity and reduce processing time, utilizing a system with a medical imaging device and processor executing these steps.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If filtered back-projection is used to correct blurring, then image clarity is improved, but processing time increases
Solution Approach 1:
The patent segments the projection calculation into direct rays (parallel to axes) and oblique rays. Direct rays are calculated efficiently using simple interpolation, while oblique rays are handled separately. This segmentation allows the majority of calculations to use the faster direct ray method, reducing overall processing time while maintaining image clarity through proper handling of oblique components.
Solution Approach 2:
The patent performs preliminary shearing of the image volume to align oblique rays with the coordinate axes before interpolation. By pre-transforming the data structure to match the ray geometry, the actual interpolation step becomes simpler and faster, avoiding the need for computationally expensive filtered back-projection while still achieving accurate reconstruction.
2Measurement precision
If regularized maximum likelihood estimation is used for noise reduction, then image quality is improved, but computational cost increases significantly
Solution Approach 1:
The patent uses simple interpolation formulas that are computationally inexpensive and can be applied rapidly to each ray. Rather than using expensive iterative maximum likelihood estimation, the invention employs disposable, low-cost calculation methods (simple linear interpolation in sheared coordinates) that achieve adequate results without the high computational burden of sophisticated statistical models.
3Productivity
If simple back-projection is used for reconstruction, then processing speed is maintained, but image blurring occurs
Solution Approach 1:
The patent changes the coordinate system parameters by shearing the image volume so that oblique rays become aligned with the coordinate axes. This parameter transformation allows simple interpolation (maintaining processing speed) to achieve results that would otherwise require complex filtering, as the sheared coordinates naturally accommodate the oblique ray geometry without introducing blur.
Data Source
AI summary
A method for interpolating at least one oblique line of response ray representing nuclear image projection data through a rectangular volume and a system for using the method. The method consists of steps of interpolating all the direct rays in a rectangular volume, making a projected ray by projecting the oblique ray onto a surface of the rectangular volume, matching the projected ray to a coinciding interpolated direct ray, shearing the rectangular volume to match the projected ray, and interpolating the oblique ray in the sheared volume.