Polynomial Approximation for MRI Conjugate Phase Reconstruction
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Solution Overview
Problem
Non-Cartesian MRI images suffer from unacceptable image degradation due to off-resonance effects caused by B0 field inhomogeneity and concomitant gradient fields, which existing fast conjugate phase reconstruction methods are unable to accurately and efficiently correct simultaneously.
Innovation Solution
A fast conjugate phase reconstruction method using polynomial approximation, specifically Chebyshev polynomials, to approximate the off-resonance phase accrual term, allowing for simultaneous correction of B0 inhomogeneity and concomitant field effects in MRI images, reducing computational cost and improving accuracy.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If direct calculation of conjugate phase reconstruction is performed to simultaneously correct B0 field inhomogeneity and concomitant gradient fields, then correction accuracy is improved, but computational time increases significantly
Solution Approach 1:
The patent transforms the complex off-resonance phase accrual term into a polynomial form by changing the mathematical parameters. Specifically, it uses the identity exp(jΔωt) = cos(Δωt) + j sin(Δωt) and applies Taylor series expansions to approximate cosine and sine functions, converting the original exponential parameter into polynomial parameters that are computationally more efficient while maintaining correction accuracy
Solution Approach 2:
The patent replaces the computationally expensive direct conjugate phase reconstruction method with a cheaper polynomial approximation method. The polynomial approximation uses pre-calculated coefficients and simple arithmetic operations instead of complex exponential calculations, providing a computationally inexpensive alternative that achieves comparable correction accuracy
2Productivity
If existing fast conjugate phase reconstruction methods are used to reduce computational cost, then computational efficiency is improved, but the ability to simultaneously correct both B0 inhomogeneity and concomitant field effects deteriorates
Solution Approach 1:
The patent modifies the mathematical parameters of the off-resonance phase term by expressing it as a polynomial in time t. This parameter transformation allows the use of efficient polynomial evaluation algorithms while incorporating both B0 inhomogeneity (Δω) and concomitant gradient field (Δωc) effects into the polynomial coefficients, enabling simultaneous correction with computational efficiency
Solution Approach 2:
The patent creates a composite correction approach by combining polynomial approximation with conjugate phase reconstruction methodology. The solution integrates multiple correction mechanisms (B0 inhomogeneity correction and concomitant field correction) into a unified polynomial framework, achieving both efficiency and comprehensive correction capability
Data Source
AI summary
A fast conjugate phase reconstruction method for MRI is based on a polynomial expansion of the off-resonance phase accrual term. The expansion is truncated and can be a Taylor or Chebyshev expansion.