Magnetic Resonance Data Reconstruction via Matrix Inversion
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Solution Overview
Problem
Conventional Fourier transform methods for magnetic resonance spectroscopy (MRS) and imaging (MRI) face limitations in reconstructing spectral or image data from time-domain signals obtained with simultaneous excitation and acquisition, particularly in situations with undersampled non-Cartesian trajectories or missing samples, leading to artifacts such as baseline artifacts.
Innovation Solution
A method that reconstructs spectral or image data using a matrix product of a reconstruction matrix and a vector of time-domain signal points, where the reconstruction matrix is calculated based on the RF excitation pulse elements and the phase accrued by the transverse nuclear magnetization, allowing direct inversion of the encoding procedure without assuming data symmetry, periodicity, or continuity, thus avoiding artifacts.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If Fourier transform methods are used for data reconstruction, then spectral or image data can be obtained from time-domain signals, but artifacts such as baseline artifacts occur in situations with undersampled non-Cartesian trajectories or missing samples
Solution Approach 1:
The patent inverts the conventional reconstruction approach by directly solving the encoding equation S = Aρ for the spin density ρ using ρ = A⁺S, where A⁺ is the pseudoinverse of the encoding matrix. This inversion approach eliminates artifacts caused by undersampling and non-Cartesian trajectories that plague Fourier transform methods, providing accurate spectral and image reconstruction without baseline artifacts or aliasing.
Solution Approach 2:
The patent replaces the mechanical Fourier transform process with a direct matrix inversion approach. Instead of using Fourier transform algorithms that assume regular sampling patterns, the invention uses linear algebra operations (pseudoinverse calculation) to directly reconstruct the spin density from the encoded signal, substituting the mathematical mechanism to achieve artifact-free reconstruction.
2Reliability
If simultaneous excitation and acquisition is performed, then detection of spins with short transverse relaxation times is enabled, but the encoding procedure becomes complex requiring advanced reconstruction methods
Solution Approach 1:
The patent segments the encoding process into a well-defined matrix operation where the encoding matrix A systematically captures the phase evolution of spins during simultaneous excitation and acquisition. By formulating the problem as a matrix equation S = Aρ, the complex physical process is broken down into manageable mathematical components that can be efficiently solved using standard linear algebra techniques.
Solution Approach 2:
The patent changes the mathematical parameters of the reconstruction approach from Fourier domain operations to time-domain matrix operations. By using the pseudoinverse of the encoding matrix A⁺ directly on the time-domain signal S, the method simplifies the reconstruction process while maintaining the ability to detect spins with short transverse relaxation times that were previously difficult to observe.
3Ease of manufacture
If Fourier transform reconstruction is used, then computational procedures are well-established, but the method assumes data symmetry, periodicity, or continuity which is not always valid
Solution Approach 1:
The patent inverts the conventional approach by directly solving the encoding equation using the pseudoinverse method rather than applying Fourier transform assumptions. This inversion approach ρ = A⁺S does not require assumptions about data symmetry, periodicity, or continuity, making it valid for undersampled and non-Cartesian trajectories while providing more accurate reconstruction results.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
This approach enables improved encoding and reconstruction of MRI/MRS data, reducing computational demands and noise sensitivity, and providing accurate representations of NMR frequencies and chemical composition, even for samples with short transverse relaxation times, without requiring constant gradients or special hardware.
Implementation Method 1
an NMR time-domain signal is created by an RF excitation pulse applied to an object in the presence of an applied magnetic field that may depend on spatial position and/or time, said time-domain signal being generated by an excited transverse nuclear magnetisation precessing about the applied magnetic field
Data Source
Figure 1(a)~1(e)
Figure 2(a)~2(b)
Figure 3
AI summary
A method for magnetic resonance spectroscopy (=MRS) or magnetic resonance imaging (=MRI) in which an NMR time-domain signal is created by an RF excitation pulse applied to an object in the presence of an applied magnetic field that may depend on spatial position and/or time, said time-domain signal being generated by an excited transverse nuclear magnetisation precessing about the applied magnetic field, whereby the RF excitation pulse is adapted to cover a whole range of NMR frequencies of interest present in the object, and time-domain signal acquisition takes place during, or during and after the application of the RF excitation pulse, is characterized in that spectral or image data are reconstructed by a matrix product of a reconstruction matrix and a vector of time-domain signal points, the reconstruction matrix being an inversion of an encoding matrix Ahα whose elements are calculated using the formula: Anα=∑m=0n-1PmeιΦnmα wherein n is the running number of a time-domain signal point, α is the running number of a discrete image or spectral element, Pm is the m-th discrete element of the RF excitation pulse in the time-domain, and Φ(n,m,α) is the phase accrued by the transverse nuclear magnetisation related to the discrete image or spectral element α in the time between the discrete RF excitation pulse element Pm and the time-domain signal point n under the influence of the applied magnetic field. The invention provides an improved method for reconstructing spectral or image data from time-domain signal acquired as describe above, which can be used more versatilely than conventional Fourier transform.