3D Radial MRI Reconstruction Without Interpolation
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Solution Overview
Problem
Conventional MRI image reconstruction methods for radial data sampling require interpolation, which can degrade image quality, and there is a need for a method to reconstruct MRI images directly from radially sampled data without interpolation.
Innovation Solution
The method involves acquiring frequency samples using a 3D radial sampling scheme and applying a spherical Fourier transform (SFT) followed by a spherical Hankel transform to directly reconstruct a 3D image in the spatial domain, utilizing spherical harmonic coefficients to accelerate computations and reduce the number of required samples.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional reconstruction methods are used for radial data sampling, then image reconstruction can be performed, but image quality degrades due to interpolation requirements
Solution Approach 1:
The patent extracts the interpolation step from the conventional reconstruction pipeline by using spherical harmonic transforms that operate directly on radially sampled data. The method removes the need for intermediate interpolation by transforming the data into spherical harmonic coefficients, performing operations in this transformed domain, and then transforming back to obtain the final image without quality loss from interpolation.
Solution Approach 2:
The patent changes the mathematical representation parameters from Cartesian coordinates to spherical harmonic coefficients. This parameter transformation allows the data to be processed in a domain where radial sampling is naturally compatible, eliminating the need for interpolation while maintaining image quality through the spherical harmonic transform framework.
2Loss of time
If the number of data samples is reduced to decrease acquisition time, then examination time is shortened, but image quality may be compromised
Solution Approach 1:
The patent moves the data processing to a different mathematical dimension by using spherical harmonic transforms. This dimensional transformation allows efficient reconstruction from fewer radial samples by operating in the spherical harmonic coefficient domain, where the data can be more effectively compressed and reconstructed without losing critical information, thus reducing acquisition time while maintaining image quality.
3Productivity
If radial data sampling is used to reduce data samples, then data acquisition time is reduced, but conventional methods require interpolation that degrades quality
Solution Approach 1:
The patent replaces the mechanical interpolation process with a mathematical spherical harmonic transform approach. Instead of mechanically interpolating radially sampled data into a Cartesian grid (which causes quality degradation), the method uses spherical harmonic transforms to directly reconstruct the image from the radial samples, substituting a complex mechanical interpolation process with an elegant mathematical transformation that preserves quality.
Data Source
AI summary
A method for spherical magnetic resonance imaging (MRI) based on three-dimensional (3D) radial data sampling. The method includes acquiring a plurality of frequency samples of an object in a spatial frequency domain according to a 3D radial sampling scheme and reconstructing a 3D image of the object in a space domain by applying a spherical Fourier transform (SFT) to the plurality of frequency samples. An MRI scanner is utilized for acquiring the plurality of frequency samples.