MR System Frequency Determination via Cost Function Minimization
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Solution Overview
Problem
Conventional methods for determining system frequency in magnetic resonance (MR) imaging are inefficient, particularly when dealing with single or unclear maxima in frequency spectra, requiring excessive computing time and being unsuitable for scenarios involving silicone.
Innovation Solution
A method utilizing a parameterized model function and cost function optimization to quickly determine system frequency by minimizing the difference between the model and acquired frequency spectra, incorporating Lorentzian functions and weighted restrictions to handle multiple substances like water, fat, and silicone.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional cross-correlation method is used to determine system frequency, then the method can handle clear dual maxima cases, but computing time increases to minutes when dealing with single maxima or silicone scenarios
Solution Approach 1:
The patent transforms the frequency determination problem from direct spectral analysis to parameter optimization. By defining a cost function that depends on parameters (frequency offset, scaling factor) and minimizing it through iterative optimization, the method achieves faster convergence. The parameterized approach allows the system to search a reduced parameter space rather than performing exhaustive spectral comparisons, resolving the contradiction between accuracy and computing time.
Solution Approach 2:
The patent performs preliminary actions by pre-defining the cost function structure and optimization algorithm before actual frequency determination. The system prepares the parameterized model and optimization framework in advance, so that during runtime, only the minimization step is needed. This preliminary setup enables the method to handle various spectral scenarios (single maxima, dual maxima, silicone presence) efficiently without requiring complex runtime decision logic.
2Reliability
If conventional method performs exhaustive search for single maximum assignment, then it can determine whether maximum belongs to fat or water, but computing time and run time increase significantly
Solution Approach 1:
The patent implements feedback through the cost function minimization process. The optimization algorithm iteratively adjusts parameters and evaluates the cost function, using the resulting feedback to guide the search toward the correct substance assignment. The cost function incorporates information about expected spectral characteristics, providing feedback that distinguishes between fat and water assignments without requiring exhaustive search. This feedback mechanism resolves the contradiction by providing reliable discrimination through iterative refinement rather than brute-force comparison.
3Adaptability or versatility
If conventional approach handles three maxima including silicone, then it can accommodate complex spectral scenarios, but computing time becomes unacceptable in the order of minutes
Solution Approach 1:
The patent creates a universal solution that handles multiple spectral scenarios (dual maxima with fat-water, single maxima, and three maxima with silicone) through a single parameterized cost function framework. The same optimization algorithm and cost function structure work across all scenarios, requiring only minor parameter adjustments rather than separate processing paths. This universality resolves the contradiction by providing adaptability through a unified approach that maintains consistent computational efficiency across diverse spectral conditions.
Data Source
AI summary
In a method, device and magnetic resonance (MR) system for determining a system frequency in MR imaging, a frequency spectrum of a region under examination is acquired. A cost function (FOM) is determined that encompasses the difference between a parameterized model function having assigned parameters that is to be optimized, and the acquired frequency spectrum. The cost function is subsequently minimized. Furthermore, the parameters of the optimized parameterized model function assigned to the determined minimum are determined and the system frequency is calculated on the basis of the determined parameters.