Variable-Density Spiral Trajectory for 2D Compressed Sensing MRI
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Solution Overview
Problem
Designing two-dimensional (2D) sampling patterns for compressed sensing in magnetic resonance imaging (MRI) with high acceleration is challenging, as existing methods like Adcock's multilevel random sub-sampling scheme are limited in their application to 2D CS MRI with high acceleration.
Innovation Solution
A method and system for 2D compressed sensing MRI using a variable-density spiral trajectory, where the sampling pattern is determined based on the distance from each sampling point to the center of k-space and a probability function, allowing for the generation of spiral gradient waveforms and tracing of a variable-density spiral trajectory for sub-sampling MRI data.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If variable-density random k-space sampling patterns are used for 3D Cartesian sampling, then data acquisition time is decreased and accuracy is improved, but the method is limited in application to 2D CS MRI with high acceleration
Solution Approach 1:
The patent applies local quality by implementing different sampling densities at different locations in k-space. The variable-density spiral trajectory concentrates sampling points near the center of k-space where signal energy is highest, and reduces sampling density toward the periphery. This localized adaptation of sampling density optimizes the balance between acquisition speed and image quality specifically for 2D CS MRI applications.
Solution Approach 2:
The patent transitions from Cartesian sampling coordinates to spiral trajectory sampling in k-space. By changing the sampling path from a grid-based Cartesian approach to a continuous spiral trajectory, the method enables high acceleration 2D CS MRI while maintaining the benefits of variable-density sampling. This dimensional transformation allows the sampling pattern to be defined by a continuous function rather than discrete grid points.
2Loss of time
If high acceleration is achieved in 2D CS MRI, then data acquisition time is reduced, but image reconstruction accuracy and structural detail preservation become challenging
Solution Approach 1:
The patent applies preliminary action by pre-planning the variable-density spiral trajectory before data acquisition. The sampling pattern is designed in advance with optimized density distribution, ensuring that critical k-space regions are sampled with appropriate density. This pre-computed trajectory guides the gradient waveforms and RF pulses during acquisition, enabling high acceleration while preserving reconstruction accuracy without requiring real-time adjustments.
3Productivity
If variable-density spiral trajectory is used for sub-sampling, then acceleration is improved and data acquisition is faster, but the complexity of generating spiral gradient waveforms and tracing trajectory increases
Solution Approach 1:
The patent replaces the mechanical approach of step-by-step trajectory calculation with an analytical solution. By defining the spiral trajectory through a continuous mathematical function in k-space, the system eliminates the need for iterative numerical methods or complex real-time computations. The gradient waveforms are generated directly from the analytical trajectory definition, significantly reducing computational complexity while maintaining high sampling efficiency.
Data Source
AI summary
In image reconstruction using a variable-density spiral trajectory, a method includes acquiring magnetic resonance (MR) data, which includes determining a multi-level undersampling pattern based on sampling distance and probability functions, and determining a desired variable-density spiral trajectory based on the undersampling pattern. Acquiring the MR data also includes generating spiral gradient waveforms based on the desired trajectory, and tracing a variable-density spiral trajectory using the spiral gradient waveforms. After tracing, the MR data can be sub-sampled based on the variable-density spiral trajectory. One or more images can be reconstructed based on the acquired MR data.