Spiral Phyllotaxis Sampling for MR Image Resolution
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Solution Overview
Problem
Existing MR imaging techniques face challenges in defining the scan order for interleaved and segmented data acquisition in three-dimensional k-space, leading to inefficiencies in compressed sensing methods.
Innovation Solution
The method arranges sample points in k-space according to spiral phyllotaxis, specifically Fibonacci phyllotaxis, ensuring a uniform distribution and simplifying the scan order, using golden angles to optimize data acquisition and employing iterative reconstruction with phase coding gradients to improve image quality and reduce artifacts.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Quantity of substance
If pseudo-random scanning or Poisson disk scanning are used in compressed sensing, then data acquisition can be reduced, but the scan order definition becomes difficult for interleaved and segmented MR data acquisition
Solution Approach 1:
The patent changes the parameter of point distribution from pseudo-random or Poisson disk patterns to spiral phyllotaxis patterns based on Fibonacci sequences. This mathematical pattern provides both uniform distribution for compressed sensing and a well-defined sequential order that is easy to implement in interleaved and segmented acquisitions, resolving the contradiction between data reduction and scan order simplicity
Solution Approach 2:
The patent employs spiral phyllotaxis patterns that follow curved spiral paths through k-space rather than straight lines or random jumps. This spiral curvature naturally provides both uniform sampling distribution and an inherent sequential order, making it suitable for compressed sensing while simplifying the definition of scan orders in segmented acquisitions
2Ease of operation
If conventional scanning procedures are used, then the scan order is easy to define, but compressed sensing cannot be effectively applied to reduce data acquisition
Solution Approach 1:
The patent transforms the traditional linear or rectangular scanning pattern into a spiral phyllotaxis pattern based on Fibonacci angles. This parameter change maintains the simplicity of sequential scanning (easy to define scan order) while enabling compressed sensing through the specific mathematical properties of the spiral pattern that provide incoherent sampling required for compressed sensing reconstruction
3Measurement precision
If more MR data are acquired to improve image quality, then resolution and signal-to-noise ratio improve, but the examination time increases
Solution Approach 1:
The patent applies compressed sensing which allows acquiring only a partial subset of k-space data (undersampling) while still reconstructing high-quality images. The spiral phyllotaxis sampling pattern ensures that the acquired partial data are distributed optimally to capture the essential image information, achieving good resolution and SNR with reduced examination time
Solution Approach 2:
The patent replaces traditional deterministic image reconstruction (Fourier transform of fully sampled data) with iterative compressed sensing reconstruction algorithms. This substitution allows reconstruction of high-quality images from undersampled data by exploiting sparsity in appropriate transforms, thereby reducing the amount of data that must be acquired while maintaining image quality
Data Source
AI summary
In a method and a magnetic resonance (MR) system to generate MR images based on an MR measurement of the magnetic resonance system, MR data are acquired in three-dimensional k-space along straight lines proceeding in parallel. Each of these lines is defined by a point in a plane which intersects each line and that is situated orthogonal to each line. The points in the plane are arranged such that a distribution of the points obeys spiral phyllotaxis.