Computer-implemented method, computer program product, computer-readable storage medium and system for improving the signal-to-noise ratio of a magnetic field profile

Abstract

The invention relates to a computer-implemented method for improving the signal-to-noise ratio of a magnetic field profile for a magnetic resonance imaging (MRI) scanner (201). The method comprises providing samples (S11, S21) of a magnetic field (M) acquired at a first time at at least two different spatial positions (X1, X2). The method comprises providing samples (S12', S22'; S12, S22) of the magnetic field (M) acquired at a second time at at least two different spatial positions (X1, X2). The samples (S11, S21, S12', S22'; S11, S21, S12, S22) are acquired by a field probe arrangement (101) while the field probe arrangement (101) is located in the magnetic field of an examination volume (V) of the MRI scanner (201).The procedure includes determining a corrected magnetic field profile (c) with improved signal-to-noise ratio based on a spatiotemporal correlation of the sampled values ​​(S11, S21, S12', S22'; S11, S21, S12, S22) and providing the corrected magnetic field profile for image reconstruction or gradient system calibration.

Description

[0001] The invention relates to a computer-implemented method, a computer program product, a computer-readable storage medium and a system for improving the signal-to-noise ratio of a magnetic field profile for a magnetic resonance imaging (MRI) device according to the independent claims.

[0002] In magnetic resonance imaging (MRI) and magnetic resonance spectroscopy (MRS), estimating or determining magnetic field gradients superimposed on a main magnetic field is of essential importance.

[0003] In MRI and MRS, the spatiotemporal field evolution is crucial for image and spectrum generation. Switched gradient fields are used for position encoding during excitation and readout, as well as for contrast and signal generation. The field evolution within the examination volume of an MRI scanner is controlled by the sequence program. This program can dynamically control resistance coils (gradient coils and active shim coils) to manage the temporal behavior of the magnetic field. Spatial encoding is controlled by activating different coils, each representing a specific field segment; for example, each gradient axis is generated by a gradient-inducing resistance coil.

[0004] Reconstructing a magnetic resonance image depends on a precise understanding of the underlying spatial and temporal magnetic field fluctuations, which can include field disturbances and vortex formation. These magnetic field fluctuations can be caused by rapid switching of gradient magnetic fields, a limited gradient bandwidth, the presence of conductive material interacting with the magnetic field, variations in tissue properties, patient displacement / movement, imperfect shielding and / or coil design, thermal effects, and / or mechanical vibrations, such as those of the gradient coils. If these fluctuations are not taken into account, they can adversely affect the image quality of the reconstructed images, specifically leading to image artifacts, signal loss, reduced resolution, and / or a lower signal-to-noise ratio.

[0005] To mitigate the effects of deviations from the expected field evolution, an established approach is to measure the spatiotemporal field in an MRI scanner and estimate a magnetic field evolution based on these measurements. The measured estimate of the field evolution within the scan volume is then used to compensate for or correct the effect of the field deviations.

[0006] Dubovan, PI, Gilbert, KM, & Baron, CA (2023). A correction algorithm for improved magnetic field monitoring with distal field probes. Magnetic Resonance in Medicine; 90:2242-2260, reveals measurements of field dynamics during a scan via "field probes".

[0007] However, due to a limited number of spatially localized measurements and the inherent noise of these measurements, field estimates can be subject to a low signal-to-noise ratio (SNR), which is reflected in the magnetic field profile. In signal processing, known or hidden dimensionality constraints and correlations can be used for noise reduction and signal quality improvement in various ways and through different algorithms.

[0008] However, current technology lacks a reliable, simple and effective improvement in the signal-to-noise ratio that enables higher resolution scans, provides a more robust and accurate method and system for reconstructing MRI images, improves operational efficiency and allows operation at lower field strengths.

[0009] The objective of the present invention is to provide computer-implemented methods, a computer program product, computer-readable storage media and a system to overcome these and other limitations and disadvantages.

[0010] One aspect of the invention relates to a computer-implemented method for improving the signal-to-noise ratio of a magnetic field profile for a magnetic resonance imaging (MRI) scanner. The method comprises providing samples of a magnetic field, in particular with or consisting of gradients of the magnetic field, which are acquired at a first time at at least two different spatial positions. The method also comprises providing samples of the magnetic field which are acquired at a second time at at least two different spatial positions. The samples are acquired by a field probe arrangement while the field probes are located within the magnetic field of an examination volume of a MRI scanner. The method further comprises determining a corrected magnetic field profile with an improved signal-to-noise ratio based on a spatiotemporal correlation of the samples.The method further includes providing the corrected magnetic field profile for image reconstruction or gradient system calibration. Optionally, the method also includes reconstructing the image or generating the gradient system calibration based on the magnetic field profile and providing an output that includes the reconstructed image or gradient calibration.

[0011] The first point in time and the second point in time are different from each other.

[0012] The term "point in time" is to be interpreted broadly and encompasses not only a precise singular moment, but also a short time window. This allows for the acquisition of a sample value by field probes located at different spatial positions within this short time window, instead of requiring all data to be acquired at a single point in time.

[0013] The spatiotemporal magnetic field profile directly incorporates the correlations of the acquired samples in space and time, unlike spatial and / or temporal correlations, which depend on only one or the other, even when these correlations are applied sequentially. This allows for the consideration of a complex spatiotemporal magnetic field profile for noise reduction. This magnetic field profile can correct distortions in the actuation pattern or caused by magnetic fields not induced in direct response to the operating program, such as magnetic field drift due to component heating, patient movement, or externally generated magnetic fields.

[0014] The magnetic field profile refers to a temporal and spatial variation of the magnetic field in the examination volume, in particular including a static magnetic field, at least one gradient magnetic field and / or a high-frequency magnetic field used during a typical imaging procedure with the magnetic resonance imaging device.

[0015] In signal processing, known or hidden dimensionality constraints and correlations can be used for noise reduction and signal quality improvement in various ways and by various algorithms, which can be employed in the present invention.

[0016] The magnetic field / phase evolution in a magnetic resonance imaging (MRI) scanner may not strictly adhere to the constraints of spatiotemporal dimensionality. This is due to actual noise in the generated fields, errors and distortions in the field generation and / or external field emission systems, as well as noise and errors in the field measurement. However, it has been found that the magnetic field / phase evolution exhibits a high statistical probability relationship between the temporal and spatial evolution of the field. Therefore, the expected magnetic field / phase evolution in the scanner exhibits a significant distortion, which can be predicted by considering the spatiotemporal correlation to determine the corrected magnetic field evolution.

[0017] It was found that the dimensionality constraints and correlations that occur in the combined spatiotemporal domain are significantly larger, more influential, and more numerous than in the time-specific domain, especially a spectral-specific domain, or the spatial-specific domain.

[0018] This method makes it possible to reliably and effectively neglect the spatially and temporally correlated noise when determining the corrected magnetic field profile with an improved signal-to-noise ratio.

[0019] The samples can include or consist of measurements of k-space positions with respect to the magnetic field and / or measurements of phase profiles of the magnetic field. The samples can be obtained by combining, in particular by integration, a multitude of measurements of the magnetic field over a sampling period, i.e., with a specific temporal resolution.

[0020] Alternatively or additionally, the computer-implemented method can be used to improve the signal-to-noise ratio of a magnetic field profile for magnetic resonance spectroscopy or electron spin resonance (ESR) methods, particularly nuclear magnetic resonance (NMR) methods and / or paramagnetic electron resonance (EPR) methods. The present method and device can be used to improve measurements from field probes, such as magnetometers or arrays thereof, operated in MRI systems for recording switched magnetic fields. The field probes may consist of or include magnetometers based on nitrogen vacancy centers (NV centers), induction-based devices such as pick-up coils or vibrating / rotating coils, atomic and optical magnetometers, superconducting quantum interference devices (SQUIDs), other quantum interference devices, and / or fluxgates.

[0021] A spatial basis set can be optimized by choosing a suitable basis set or adapted to specific systems or sequences, for example, by truncating combinations of different orders of spherical harmonics. The number of basis functions in the actual projection can be equal to or less than the number of positions in the field measurement. Projecting onto a smaller number of spatial degrees of freedom can improve the conditioning of the inversion of P and thereby reduce noise and errors in the field estimation.

[0022] In known approaches to field monitoring, the calculation of the magnetic field in the volume has been discussed under two different assumptions. First, the temporal evolution at every spatial point in the region of interest (ROI) is bandwidth-limited at a frequency significantly higher than the bandwidth of the gradient and active shim system of the MRI scanner 201. Second, this spatial footprint is harmonic in space and of limited degrees of freedom. To achieve this, the field evolution is projected onto a finite set of spatial basis functions, and the temporal field evolution (of all components) is filtered with a single filter in the time dimension.

[0023] However, the number of spatiotemporal degrees of freedom for field development within the study volume V is subject to far more constraints. In general, these degrees of freedom do not lie entirely within the projection space of the separate temporal filters and spatial adjustments used according to the state of the art.

[0024] The first time point is measured in a time interval that contains a first dynamic with a multitude of samples from the field probe array, and the second time point lies in a time interval that contains a second dynamic with a multitude of samples that differ from the first dynamic.

[0025] This makes it possible to consider correlations, especially spatial-temporal correlations, between samples of different time-separated dynamics.

[0026] The dynamic range can comprise a multitude of samples acquired over a time interval at a multitude of different spatial positions. The majority of dynamic ranges can be acquired at the same spatial positions at different time intervals, and indeed at various pluralities of different spatial positions within those time intervals. Even when multiple sets of samples of a dynamic range are acquired at different spatial positions within the same time interval, the samples of that dynamic range can still be spatially and temporally correlated. For example, a sample acquired at a first spatial position at the beginning of the dynamic range can be spatially and temporally correlated with a sample acquired at a second spatial position at the end of the dynamic range.

[0027] These dynamics can differ significantly from one another. An example of a significantly different dynamic can be a difference resulting from the magnetic resonance imaging (MRI) system changing its nominal gradient output during image encoding, particularly in a predetermined manner, e.g., due to different contrast encoding or a different k-space step. The nominal gradient output of the MRI system can be the nominal gradient output prior to the application of eddy current correction. For example, the MRI system can change its nominal gradient output in time prior to dynamic acquisition, particularly at most 2 s prior, more specifically 20 ms prior, preferably at most 2 ms prior, which can still be detected during dynamic acquisition. Alternatively, the nominal gradient output can be changed during dynamic acquisition.

[0028] Another example of the dynamics differing significantly from one another can be a difference resulting from the magnetic resonance imaging device changing its nominal gradient output after the eddy current correction stage of the MR system (gradient pre-emphasis) during the acquisition of the dynamics, particularly in a predetermined manner, for encoding an MRI image at a distance of no more than 20 cm from an isocenter of the MR device by at least 50 µT, in particular 1 µT, preferably 0.05 µT.

[0029] Another example of how the dynamics can differ significantly is that the difference in the magnetic field profile between two dynamics at any given time during the dynamics at any spatial point in the MR device at a distance of no more than 20 cm from an isocenter of the MR device is at least 50 µT, in particular 1 µT, preferably 0.05 µT.

[0030] Another example of the fact that the dynamics differ significantly from one another can be that the difference in the phase evolution of a proton spin with respect to the difference in the magnetic field profile between two dynamics at any time during the dynamics at any spatial point in the MR device at a distance of at most 20 cm from the isocenter of the MR device is at least 1 rad, in particular 0.25 rad, preferably 0.05 rad.

[0031] Alternatively or additionally, the dynamics, which differ significantly from each other, can be caused by the drift behavior of the MRI system, in particular its main magnet and the gradient / shim field generating devices, or by fields induced by the movement of the patient, breathing, etc.

[0032] The dynamics that differ significantly from each other can be selected from one or more of the previously mentioned examples of significantly differing dynamics.

[0033] The sampled values ​​of the dynamics can be acquired with a temporal resolution of 1 ns to 1 ms, in particular 0.5 µs to 100 µs, preferably 1 µs to 10 µs.

[0034] The dynamics can be recorded at a multitude of spatial positions over a predetermined time interval. Multiple dynamics can be recorded sequentially in successive time intervals, which may optionally be of the same length. The time interval for recording an entire dynamic can be selected between 0.1 ms and 10 s, in particular between 0.1 ms and 100 ms, preferably between 0.5 ms and 80 ms.

[0035] This temporal resolution and / or this specified time interval can enable an adequate determination of the magnetic field profile on time scales that are relevant for the spatial coding and / or the rapid change of magnetic fields.

[0036] Each of the field probes in the field probe array can be configured to acquire sample values ​​at a specific spatial position.

[0037] At least one of the field probes for acquiring samples at different spatial positions can extend over a spatially extended area. A first field probe can be configured to acquire samples over a first spatially extended area. A second field probe can be configured to acquire samples over a second, spatially extended area. The first and second extended areas can be different from each other. The first and second field probes can be located at different spatial positions, in particular at spatially overlapping positions. Spatial resolution of the acquired samples at the corresponding spatial positions can be achieved by known methods for encoding spatial resolution, e.g.,by switching gradient fields for phase / frequency, layer coding, or by using spatially limited radio frequency transmission, receiving fields, or combinations thereof.

[0038] The first time point may lie within a dynamic range encompassing a large number of samples from the field probe array, and the second time point may lie within the same dynamic range.

[0039] This makes it possible to consider the correlations, especially the spatiotemporal correlation, of different samples within the same dynamic range. Considering these different samples within the same dynamic range can allow the magnetic field profile to be corrected for correlated noise, particularly on small timescales.

[0040] The method can include providing at least one first dynamic range with a plurality of samples and a second dynamic range with a plurality of samples acquired at different time intervals. The method can include synchronizing the time intervals for dynamic range acquisition with the operation of the magnetic resonance imaging (MRI) system. The time intervals and the operation can be synchronized such that at least one parameter that defines or contributes to magnetic field generation is synchronized with the dynamic range acquisition time intervals.

[0041] This allows for the inclusion of correlations across the entire dynamic range, encompassing a large number of samples, to improve the signal-to-noise ratio. This, in turn, enables the identification of more relevant spatiotemporal correlations based on synchronization with magnetic field generations between successively acquired samples of different dynamic ranges.

[0042] Synchronizing the selection of time intervals for dynamic range acquisition with the operation of the magnetic resonance imaging (MRI) scanner improves the consistency and validity of the acquired spatiotemporal correlations with respect to a magnetic field profile during standard MRI operation for image acquisition. Samples of these dynamic ranges, acquired at synchronized time intervals, allow for the identification of these correlations while simultaneously reducing sample variability, thus enabling noise discrimination in a more effective and reliable manner.

[0043] The method may include receiving a measurement trigger signal from the magnetic resonance imaging (MRI) scanner, enabling the synchronized selection of the time interval(s). The method may also include sending a measurement trigger command to the MRI scanner to initiate the measurement, which may further facilitate the synchronization of the time interval(s) with the one or more parameters that define or contribute to the magnetic field. Sampled values ​​may be acquired in response to the received measurement trigger signal or the sent measurement trigger command.

[0044] The operation of the magnetic resonance imaging device can be a temporally sequenced operation that follows a specific temporal sequence of activations, in particular to achieve a similar or substantially the same magnetic field in the examination volume for the different time intervals.

[0045] The at least one parameter that defines or contributes to the magnetic field generation can be a parameter that specifies the magnetic field generation of at least one gradient coil, one high-frequency coil and / or one component of an active shim system of the magnetic resonance imaging device.

[0046] The sampled values ​​and / or the dynamics can be captured at at least 3 different spatial positions, in particular at at least 4 different spatial positions, preferably at at least 16 different spatial positions, or are captured during the process.

[0047] Acquiring samples at at least three different spatial positions improves the reliability and robustness of the corrected magnetic field profile, taking into account magnetic field variations and their correlations across the scan volume. More spatial positions allow for a more accurate estimation of the magnetic field profile, but space within an MRI scanner is limited, restricting the number of field probes that can be placed within the scan volume. In particular, at least 16 different spatial positions enable optimized use of space for determining the corrected magnetic field profile while maintaining a manageable computational effort for calculating the spatiotemporal correlation.

[0048] Determining the corrected magnetic field profile may involve applying a dimensionality reduction algorithm to the samples / dynamics to achieve noise reduction, in particular (i) a principal component analysis algorithm, a singular value decomposition, or a singular spectral analysis, and / or (ii) a dimensionality reduction algorithm, a locally linear embedding (LLE), a kernel principal component analysis, a kernel-independent principal component analysis, a wavelet-based principal component analysis, a wavelet-based independence analysis, isometric mapping (isomap), t-distributed stochastic neighbor embedding (t-SNE), uniform manifold approximation and projection (UMAP), autoencoders, machine learning, proper orthogonal decomposition, dynamic mode analysis, or a spatiotemporal Autoencoder,a spatiotemporal convolutional neural network, a spatiotemporal graph neural network, a nonlinear independent component analysis, a spatiotemporal variational autoencoder and / or a spatiotemporal cluster analysis algorithm.

[0049] Several of these dimensionality reduction algorithms enable nonlinear dimensionality reduction to capture the most relevant spatiotemporal correlations. Principal component analysis provides an efficient linear dimensionality reduction method suitable for modeling magnetic field fluctuations, which can typically be reliably modeled by harmonic functions. Kernel principal component analysis can further enable nonlinear effects in dimensionality reduction. Linear dimensional analysis (LLE) can preserve local relationships, i.e., capture locally correlated noise. Isomap can preserve the intrinsic geometry of the data. SNE, particularly t-distributed SNE, can preserve local structures of the data. UMAP enables improved preservation of global and local structures and is computationally fast.Autoencoders enable the capture of complex noise patterns by neural networks, providing highly customizable and powerful dimensionality reduction.

[0050] Dimensionality reduction can be applied to the dynamics that include samples of the gradient magnetic field, the integral of the gradient magnetic field, or k-space coefficients.

[0051] The dimensionality reduction achieved through the principal component analysis, singular value decomposition, or singular spectral analysis algorithm can be selected to enable noise suppression of the corrected magnetic field profile, particularly by selecting only principal components greater than or equal to a sample value, and especially by selecting a threshold value dependent on the samples or a predefined threshold value. A noise-reduced field expansion can be calculated by specifically weighting singular values, particularly by weighting them in a predefined manner.

[0052] This, especially the predefined threshold, enables targeted adjustment of the principal component analysis to reliably reduce spatially and temporally induced noise.

[0053] Singular value decomposition can be performed using the optimal shrinkage method for singular values. The sampling-dependent threshold can be determined using the Marchenko-Pastur law or the Gavish-Donoho law.

[0054] This allows for the selection of a data-dependent threshold for the number of principal components to be retained and the filtering out of noise-dominated components, thus enabling robust noise suppression.

[0055] For the Marchenko-Pastur method, the density of this distribution for an interval λ in [λ min , λ max ]: ρ(λ)=12πcσ2(λmax−λ)(λ−λmin)λ,with λmin=σ2(1+c)2, λmax=σ2(1+c)2

[0056] The parameter c=mn denotes the ratio of the dimensions m to the number of samples n. λ denotes the eigenvalues.

[0057] For the Gavish-Donoho method, the formula for the optimal threshold is: λ*=σ(n+m) or λ*=σ(1+mn) For large matrices and m ≤ n, where σ is the standard deviation, m is the number of rows, and n is the number of columns. The standard deviation σ can be approximated by the median of the singular values ​​of the data.

[0058] In the optimal shrinkage method, the optimal weighting method depends on the desired norm to be minimized. For example, in the case of Frobenius norm loss, the optimal nonlinear weighting is: η∗(σ)=1σ(σ2−B−1)2−4B if σ≥1+B η∗(σ)=0 if σ≤1+B

[0059] The parameter B denotes the ratio of the dimensions of the matrix (smallest dimension / largest dimension).

[0060] The sampled values ​​can be acquired at at least two different pluralities of different spatial positions by positioning the field probe arrangement in the magnetic field of the investigation volume at at least a first and a second position and / or orientation that differ from each other.

[0061] These first samples and the second samples, acquired at different positions / orientations, allow for a more accurate estimation of the magnetic field by interpolating these localized first and second samples. For example, a limited basis set of harmonic functions, such as spherical harmonics, can provide a more accurate estimation of the magnetic field distribution based on these localized first and second samples. The order of the basis set can be equal to or less than the number of spatial positions at which the samples are acquired.

[0062] The first and second positions / orientations are different. The scan values ​​can be acquired in a known manner by moving / rotating the field probe array and / or a component of the MRI scanner within the scan volume, e.g., by moving along a specific path or rotating through a specific angle.

[0063] The method can be used in conjunction with a calibration measurement using the field probe array without a patient in the examination volume to determine a compressed basis. The method can involve receiving the compressed basis in a spatiotemporal domain, particularly the spatiospectral domain. The compressed basis can be derived from (i) a partial-area measurement, (ii) a pre-scan measurement, or (iii) the calibration measurement. The method can further include applying the compressed basis to reconstruct an image or to generate a gradient calibration.

[0064] This provides a baseline measurement that can capture MRI-device-specific magnetic field variations that affect image quality, and especially noise. Furthermore, the calibration measurement without the patient can avoid patient-induced variations. Determining a set of base functions with the patient in the scan volume and the compressed baseline based on the calibration measurement without the patient can filter between noise and artifacts caused by the device and relevant patient-induced data.

[0065] The spatiotemporal correlation can be based on measured or derived properties of the magnetic resonance imaging device, in particular (i) a linear transfer function and / or a nonlinear transfer function of the magnetic field, (ii) derived system properties of a shim system and / or (iii) at least one nominal sequence information selected from a nominal gradient timing control, a nominal repetition time, an echo time and / or a nominal bandwidth.

[0066] In this way, the determination of the corrected magnetic field profile based on the spatiotemporal correlation, which relies on the properties specific to the magnetic resonance imaging device, can be improved.

[0067] The computer-implemented method can involve applying a noise reduction kernel to temporally and / or spatially adjacent samples, e.g., the dynamic range samples acquired over the specified time interval, to reduce the input noise. The noise reduction kernel can be selected from a Gaussian, median, Sobel, or bilateral kernel.

[0068] In a spherical harmonic approximation, the derived properties of the magnetic resonance imaging (MRI) device, represented by at least one set of transfer functions, can influence the harmonic components differently. For example, the transfer functions can modify the amplitude / phase of the various harmonic components to varying degrees.

[0069] An active shim system can enable fine-tuning to compensate for distortions and generate a more controlled magnetic field. In this way, derived system properties of a shim system can be used to determine the spatiotemporal correlation.

[0070] Determining the corrected magnetic field profile can involve applying a noise reduction filter to the magnetic field profile or to the sampled values / dynamic range(s) in the spatiotemporal domain. The filter can be selected from a Wiener filter, a Kalman filter, a convolutional neural network filter, and / or a Savitzky-Golay filter.

[0071] These multivariate filters, meaning those that combine spatial and temporal aspects, enable reliable filtering across the spatiotemporal domain, thus improving the signal-to-noise ratio. Other filters include a vector median filter, a vector direction filter, a multichannel anisotropic diffusion filter, and / or a bilateral filter for multivariate data.

[0072] The method can include the application of at least one domain-specific filter, preferably a spatially domain-specific filter and / or a temporally domain-specific filter, to the magnetic field profile or to the sampled values / dynamics(s).

[0073] This allows the method to selectively reduce not only the spatially and temporally correlated noise, but also the spatially specific correlated noise and / or the temporally specific correlated noise. Applying an additional filter in at least one of the two domains, the spatial and / or the temporal domain, ensures more stable or smoother sample values ​​in the spatial and / or temporal domain, further reducing noise.

[0074] This at least one univariate domain-specific filter can be selected from a Fourier transform-based regularization, in particular a low-pass filter, a high-pass filter, a band-pass filter and / or a wavelet filter, a Kalman filter, an averaging filter, a recursive filter, a Gaussian filter, a median filter, averaging filter, a Wiener filter, a convolutional neural network filter and / or a Savitzky-Golay filter.

[0075] The determination of the corrected magnetic field profile or the linear or nonlinear spatiotemporal filter based on the spatiotemporal correlation can be carried out by training a supervised or unsupervised machine learning model, in particular a neural network, preferably a spatiotemporal convolutional neural network, optionally a residual neural network.

[0076] This machine learning model can enable automated and adaptive noise optimization by modifying the sample values / dynamics and / or the magnetic field profile, resulting in data-driven improvement. The machine learning model can be imaging system-specific, meaning it can be specifically adapted for noise reduction on a particular type of magnetic resonance imaging (MRI) scanner, and especially for a variety of different MRI scanner types. Input of this type can be received throughout the process.

[0077] Another aspect of the present invention relates to a computer program product which, when the program is executed by a computer, causes the computer to perform the steps of the previously described computer-implemented method.

[0078] Another aspect of the present invention relates to a computer-readable storage medium containing instructions which, when executed by a computer, cause the computer to perform the steps of the computer-implemented method described above.

[0079] Another aspect of the present invention relates to a system comprising the field probe arrangement, in particular a magnetic resonance tomography or spectroscopy device, and a processing unit configured to carry out the computer-implemented method described above.

[0080] The field probe arrangement can comprise an array of field probes spaced apart at spatial positions within the examination volume of the magnetic resonance imaging (MRI) or spectroscopy device. This allows for the estimation of the spatial behavior of the magnetic field over time and / or the spatial behavior of the time integral of the magnetic field.

[0081] The field probe(s) can directly or indirectly (e.g., by time integration or differentiation) measure the magnetic field profile, its magnitude, or its components at a location based on various physical principles. Known principles of such magnetometers relate to nuclear, electron, or atomic / molecular spins or moments, as in NMR / EPR or ferro / ferri magnetic resonances, which are detected inductively, particularly using NMR / EPR field probe(s), Overhouser magnetometers, optical detectors, preferably NV centers, or atomic magnetometers. The field probe(s) can be functionally adapted to acquire samples based on the Hall effect, magnetoresistance, induction in stationary or moving (vibrating or rotating) loops or coils, quantum interference of particles (e.g., Aharanov-Bohm) or superconducting states (e.g., in SQUIDs), optical effects (e.g.,based on Kerr or Faraday magnetometers) or the saturation of ferro- / ferromagnetic materials (e.g. fluxgates).

[0082] The field probes can be NMR or EPR field probes containing an aqueous solution and / or at least one lipophilic component, particularly at least in the vicinity of means for NMR or EPR excitation and / or detection. The smallest dimension of an NMR / EPR-active region of the active medium is preferably selected from one of the following ranges: 0.2 mm to 0.7 mm, 0.7 mm to 1.1 mm, and 1.1 mm to 2 mm.

[0083] The invention further enables the simultaneous optimization of a field probe dimension, its arrangement within the field probe array, and the noise reduction. The number of field probes in the field probe array can be optimized. The field probes can also be selected to optimize cost, size, area, volume, resolution, and / or sensitivity for an application that utilizes knowledge of the noise reduction algorithm's effect. In particular, the size / area / volume of a field-sensitizing unit can be reduced to achieve higher spatial resolution and robustness by compensating for the resulting loss of sensitivity or signal-to-noise ratio (SNR) through the noise reduction algorithm.

[0084] Furthermore, the volume of active media of NMR or EPR field probes can be reduced, to a first approximation, by the factor of the SNR improvement in the final field estimation of the noise suppression algorithm compared to an embodiment without a noise suppression algorithm, compared to NMR or EPR field probes operating without noise suppression at comparable field strength.

[0085] The aforementioned means for NMR / EPR excitation or detection may include circuits tuned to a magnetic field strength in the range of 0.1 to 25 T, in particular 0.4 to 15 T.

[0086] In some embodiments, the size / volume of the active NMR / EPR media is chosen to be large enough that the SNR / image quality of the MR images from certain applications, reconstructed based on field information derived from the field probe array and the denoising step, is not impaired. Impairment means that the SNR of the reconstructed images or the sample values / dynamic range(s) is degraded by no more than 15%, preferably 5%, and particularly 1%.

[0087] In a typical embodiment, NMR / EPR field probes can be specifically optimized for a magnetic field strength provided by the MRI system. This is achieved by tuning the NMR / EPR excitation and / or detection circuitry to the resonance frequency of the NMR-active nucleus at the aforementioned magnetic field strength of the MRI scanner.

[0088] Another aspect of the present invention relates to a computer-readable storage medium containing the corrected magnetic field profile with improved signal-to-noise ratio based on a spatiotemporal correlation that can be obtained by the computer-implemented method described above.

[0089] The method also enables improved differentiation between relevant signals and noise by taking into account correlations across different input data, in particular input data acquired at different nominal gradient outputs of a magnetic resonance imaging device.

[0090] Another aspect of the present invention relates to a computer-implemented method for improving the signal-to-noise ratio of a magnetic field profile for a magnetic resonance imaging (MRI) scanner, particularly as described above. The method comprises providing a first dynamic range comprising a plurality of first samples of the magnetic field, which in particular include or consist of gradients of the magnetic field that are distinct from one another. The method also comprises providing a second dynamic range comprising a plurality of second samples of the magnetic field that are distinct from one another. The samples are acquired by a field probe arrangement located in the magnetic field of an examination volume of the MRI scanner. The first and second dynamic ranges differ substantially from one another.The procedure involves determining a corrected magnetic field profile with an improved signal-to-noise ratio based on a temporal correlation of the first and second dynamics.

[0091] This method represents a simple, reliable, efficient, and time-saving computer-implemented procedure that reliably reduces noise and improves data quality, thereby amplifying the relevant signal within the data. In particular, the method makes it possible to detect and account for hidden noise patterns, such as noise anomalies and inherent noise structures in the data.

[0092] This method offers a solution for minimizing noise while considering a significantly different dynamic. This allows gradual shifts in sampled dynamic values, corresponding, for example, to be associated with relevant signals, while uncorrelated shifts can be more easily identified as noise.

[0093] The field probe arrangement for recording the dynamics can comprise one or more field probes at corresponding spatial positions, optionally field probes at at least 2 different spatial positions, in particular at at least 3 or 4 different spatial positions, preferably at at least 16 different spatial positions.

[0094] These dynamics can be captured in disjoint time intervals and, in particular, for the same spatial positions or different spatial positions.

[0095] The method may further include providing the corrected magnetic field profile for image reconstruction or gradient system calibration. The method may include reconstructing the image or generating the gradient system calibration based on the corrected magnetic field profile and providing an output containing the reconstructed image or gradient calibration.

[0096] The dynamics that differ significantly from each other can be selected from one or more of the previously mentioned examples of dynamics that differ significantly from each other.

[0097] The sampled values ​​can include or consist of measurements of the magnetic field magnitude, measurements of magnetic field coefficients and / or k-space coefficients with respect to the spatial magnetic field evolution in conjunction with spatial basis functions, in particular polynomial and higher-order polynomial basis functions, measurements of the phase evolution of a spin with respect to the magnetic field evolution in the investigation volume (V), and / or measurements of the phase evolution of the signal from an NMR or EPR field probe. The sampled values ​​can be obtained by combination, in particular by forming a time integral or derivative over a multitude of measurements of the magnetic field over a sampling period, i.e., with a specific temporal resolution.

[0098] Temporal correlation can be at least a partial temporal correlation of a large number of samples with the same dynamics.

[0099] The first and second dynamic ranges can each comprise samples acquired at a variety of different spatial positions. The first dynamic range can be acquired at at least one different spatial position than the second dynamic range, or at the same spatial position(s) as the second dynamic range.

[0100] The method can include synchronizing the time intervals for dynamics acquisition with the operation of the magnetic resonance imaging (MRI) system. The time intervals and the operation can be synchronized such that at least one parameter that defines or contributes to magnetic field generation is synchronized with the dynamics acquisition time intervals.

[0101] The procedure can include receiving a measurement trigger signal from the magnetic resonance imaging (MRI) scanner, enabling the synchronized selection of the time interval(s). The procedure can also include sending a command to initiate the measurement to the MRI scanner, which can further facilitate the synchronization of the time interval(s). The dynamic range samples can be acquired in response to the received measurement trigger signal or the sent measurement trigger command.

[0102] The operation of the magnetic resonance imaging (MRI) scanner can be time-sequenced, following a specific sequence. This process allows for different, but similar, magnetic fields to be achieved within the scan volume at different time intervals.

[0103] The method can include providing an initial set of dynamic data, acquired at various spatial locations during a first time interval. The method can also include providing a second set of dynamic data, acquired at different or the same spatial locations during a second time interval.

[0104] The invention will now be described with reference to certain embodiments and figures which show: Fig. 1: An embodiment of a system according to the invention, comprising a plurality of field probes of a field probe arrangement connected to a processing unit. The field probe arrangement and preferably parts of the processing unit are located in or around the examination volume of a magnetic resonance imaging or spectroscopy device. Fig. 2A: a schematic representation of a pulse sequence of switched magnetic fields generated by an MRI scanner and the dynamics detected by a field probe in the MRI scanner, Fig. 2B: a schematic representation of spatiotemporal correlations of sampled values ​​of a dynamics recorded over a time interval, Fig. 2C: a schematic representation of spatiotemporal correlations of sampled dynamics recorded over different time intervals, Fig. 2D: a schematic representation of temporally correlated dynamics that were recorded sequentially, Fig. 2E: a schematic representation of temporally distinct sequences of dynamics comprising a multitude of samples acquired at different spatial positions, and exemplary correlations between the samples and dynamics, Fig. 3: a schematic block diagram and corresponding graphs showing spatiotemporal magnetic field generation and the determination of an estimate of the spatiotemporal magnetic field, i.e., the magnetic field profile, based on spatially localized sample measurements, Fig. 4A - 4G: exemplary graphically represented data illustrating the effect of noise reduction using a singular value decomposition algorithm, taking into account spatiotemporal correlations, Fig. 5A and Fig. 5B: an exemplary dataset of mean squared error and maximum error of the magnetic field estimation in a field of view of a field probe arrangement, obtained on the basis of a prior art approach by applying a projection and a low-pass filter, Fig. 5C and Fig. 5D: the exemplary dataset of Fig. 5A and Fig. 5B of the mean squared error and the maximum error of the magnetic field estimation in the field of view of the field probe array, obtained on the basis of a regularized inversion approach, i.e. taking into account the spatiotemporal correlation, and Fig. 5E and Fig. 5F: a ratio of the signal-to-noise ratios of the previously described approaches of Fig. 5C and Fig. 5D in relation to the Fig. 5A and Fig. 5C or 5B and Fig. 5D.

[0105] Fig. Figure 1 shows an embodiment of a system 301 according to the invention. The system 301 comprises a plurality of field probes 21, 22, 23, 24, 25, 26, 27 of a field probe arrangement 101, which are connected to a processing unit 3. The field probes 21-27 of the field probe arrangement 101 are arranged in an examination volume V of a magnetic resonance imaging (MRI) device 201. The field probes 21-27 are arranged at different spatial positions X1, X2 within the examination volume V and are configured to acquire samples of the magnetic field. The temporal resolution, i.e., sampling rate, is 10 µs. A dynamic range comprising a plurality of samples 21-27 for each spatial position X1, X2 is, for example, collected over a predetermined time interval of 80 ms. The operation of the magnetic resonance imaging device is preferably synchronized with the time intervals for recording the dynamics.For example, each field probe 21 - 27 can acquire a series of samples at its spatial position X1, X2 during the entire time interval, while the magnetic resonance imaging device is operated in a specific temporal sequence, e.g. in a specific spatial coding operation.

[0106] The field within the investigation volume V can be estimated using field probes 21-27, which are formed by magnetometers arranged around or within the investigation volume V. Although these field probes 21-27 measure the temporal evolution of the field only at a finite set of discrete spatial positions X1, X2, the field on the side of the investigation volume V can be estimated based on established methods of spatial interpolation. These spatial interpolations utilize the fact that the field distribution in the quasi-stationary region of magnetism must be represented by a harmonic function in a spatial domain. Furthermore, there is a limited degree of freedom in the spatial field distribution of the dynamic magnetic field that prevails in the investigation volume V.

[0107] Mathematically speaking, this spatial interpolation is achieved by projecting the field measurements obtained at discrete positions onto a limited basis set of harmonic functions. (ψn(r→)), e.g. spherical harmonics: B(r→,t)=∑n=0Nan(t)⋅ψn(r→) a n (t) refers to a temporal development of a field distribution ψn(r→), which is defined as: an(t)=∑p(P+)n,pBrp(t) or a(t) = P + B r (t) in vectorized form with (a(t)) n = a n (t) and (B(t)) p = B rp (t). P = ψ n (r p ) encodes the positions of the field probes, “+” denotes a suitable (pseudo-)inverse and B rp (t) denotes the time-dependent magnetic field profiles measured by the field probe in r p be measured.

[0108] It should be noted that the spatial basic functions described here as harmonic ψn(r→) Strictly speaking, these principles are only optimal when calculating the evolution of the magnetic field. In practice, however, this principle can be applied to the phase evolution of the spin signal phase. The magnetic field and the phase are related to each other through integration in the time domain. The precession frequency of NMR and EPR scales linearly with the strength of the magnetic field, i.e., the norm of the magnetic field vector at the location of the spin. Therefore, the phase caused by this precession in response to the superposition of (vector) magnetic fields can be nonlinear with respect to the field superposition. Consequently, the spatial distribution of this phase increase can be nonharmonic in nature.Spatial basis functions that reflect this effect, typically referred to as the companion field effect, can be added in the spatial expansion or used to improve the spatial interpolation of the phase distribution in the imaging / spectroscopy volume.

[0109] The term “spatial-temporal” degrees of freedom therefore means degrees of freedom that can be described neither solely in the temporal nor solely in the spatial domain; i.e., a filter that essentially projects onto such degrees of freedom cannot be separated into the spatial and temporal domains.

[0110] Fig. Figure 2A shows a schematic representation of a sequence of (generally) spatially nonlinear magnetic fields of an MRI scanner and dynamics D1, D2, comprising samples S11, S12, S11', S12' acquired by a field probe in the MRI scanner. The sequence blocks, consisting of a multitude of samples S11, S12 and S11', S12' acquired at a constant sampling rate of 10 µs over a time interval of 80 ms, each denote a dynamic D1, D2.

[0111] The limitation of field development in an MRI device 201 (see Fig. 1) The effect on spatiotemporal degrees of freedom is caused by various mechanisms. In most cases, the process program requires a highly structured field development in both time and space. One limitation is that MRI and magnetic resonance spectroscopy (MRS) sequences are often very repetitive or nearly so.

[0112] An upper subsection of Fig. 2A_1 shows non-uniform magnetic fields generated by an MRI system over an extended period. The sequence of Fig. 2A uses a sequence of magnetic field drives with a repetition time TR. The magnetic field drives are essentially repeated for each repetition time TR, meaning they result in a highly correlated / similar non-uniform magnetic field drive for acquiring k-space lines of the image, different slices, averages, or a series of images. The non-uniform magnetic field can exhibit different patterns (e.g., polygonal shapes, especially trapezoids and / or sinusoids). This behavior can be expressed, for example, in terms of autocovariance and cross-covariance functions (correlation). The repetition times TR of Fig. 2A_1 are of equal length and synchronized with parameters that control the operation of the MRI device and define the non-uniform magnetic fields generated by the MRI device. Therefore, the two non-uniform magnetic fields of these repetition times TR are Fig. 2A_1 are similar to each other. These non-uniform magnetic fields of these repetition times TR can only differ by addition or scaling of fundamental waveforms, such as polygonal waveforms, in particular trapezoidal and / or sine waveforms.

[0113] A middle section Fig. 2A_2 of Fig. Figure 2A shows the acquired dynamics D1, D2, each comprising a multitude of samples S11, S12, S11', S12', acquired, for example, at a constant sampling rate of 10 µs over a time interval of 80 ms. The dynamics D1, D2 were acquired in time intervals I1, I2 synchronized with an electromagnetic actuation of the MRI scanner; that is, the time intervals I1, I2 refer to corresponding sub-segments or the entirety of the repetition time interval TR, which comprises a similar or identical electromagnetic actuation to achieve the non-uniform magnetic field.

[0114] Fig. Figure 2A shows an example of the acquisition of the dynamics D1, D2 via the field probe at a single spatial position X1.

[0115] Similar to in Fig. As shown in 2E, however, a dynamic D1, D2 / sample values ​​S11, S12, S12', S21, S22' can be captured at a multitude of spatial positions in addition to different time intervals I1, I2.

[0116] The lower section Fig. 2A_3 of Fig. Figure 2A shows an estimate of the non-uniform magnetic field, measured using the field probe arrangement based on the respective dynamics D1 and D2. This estimate of the non-uniform magnetic field is an approximation of the actual non-uniform magnetic field for the respective time interval I1 and I2. The magnetic field profile can be determined based on these estimates of the non-uniform magnetic field.

[0117] Since MRI scanners are stable to a certain degree, it can be assumed that the aforementioned relationships—i.e., one or more parameters that define or contribute to the magnetic field generation—are reflected in the actual magnetic field profile and thus in the magnetic field measurements. For example, the fact that the required field profile is similar in each time interval I1 and I2 must be reflected in the data and the corrected magnetic field profile.

[0118] The field control of the MRI device (gradient chain and shim chain, consisting of numerical waveform generation, eddy current compensation, digital-to-analog conversion, amplification, filtering and gradient coil control) restricts the degree of freedom of the spatiotemporal magnetic field profile that can be achieved during magnetic field generation.

[0119] MRI scanners have a limited bandwidth (typically in the range of a few tens of kHz), which restricts the degrees of freedom in the time domain. This can be used to denoise samples from magnetic field measurements by low-pass filtering the acquired time-domain magnetic field data with a cutoff frequency close to the bandwidth limit of the magnetic field actuators. However, the limitation of degrees of freedom imposed by the MRI scanner's electromagnetic drive system extends even further, as shown by the higher-order transfer functions for each drive channel. These transfer functions imply that actuating each channel at any given frequency produces only one distinct spatial-spectral (and thus spatiotemporal) field output response.The magnetic field measured by the field probe arrangement in the MRI device is therefore likely to follow a spatiotemporal manifold that is determined by the transfer function of each electromagnetic actuation system.

[0120] However, there are magnetic field profiles in an MRI scanner that are not induced by the sequence program or the triggering hardware, but rather by heating transients of the components involved, subject movements, or external sources such as power lines, electric motors, or other MRI components. These emissions typically have known power spectra, leading to correlated shifts in the sampled values ​​of magnetic field measurements. For example, temperature and other magnetic shifts are known to be very slow compared to the activation of the gradient fields. Furthermore, subject movements are usually limited to a few tens of Hz and can exhibit very distinct peaks in their spectrum, which are related to heart rate and respiration.

[0121] Fig. Figure 2B shows a schematic representation of the spatiotemporal correlations of the samples S11, S12, S21, S22 of a dynamic range D1, D1', which was recorded over a time interval I1. This correlation is indicated by the black arrows, which represent the samples S11, S12, S21, S22 from the subsections. Fig. 2B_1 and Fig. 2B_2 of Fig. Connect 2B. The dynamics D1, D1' are captured for two different spatial positions X1, X2.

[0122] Fig. Figure 2C shows a schematic representation of the spatiotemporal correlations of the samples S11, S12', S21, S22' of the different dynamics D1, D1'; D2, D2', which were recorded at different time intervals I1, I2. This sequence of dynamics D1, D1'; D2, D2' was recorded for different spatial positions X1, X2. The spatiotemporal correlations are illustrated by the black arrows, which represent these samples S11, S12', S21, S22' of the subsections. Fig. 2C_1 and Fig. 2C_2 of Fig. Connect 2C.

[0123] Fig. Figure 2D shows a schematic representation of the time-correlated dynamics D1, D2, which were acquired sequentially over different time intervals I1, I2, each comprising a multitude of samples S11, S12; S11', S12'. The sequence of dynamics D1, D2 in Fig. 2D is captured at only one spatial position X1. The temporal correlation is exemplified by a dashed arrow connecting the two dynamics D1 and D2. Furthermore, the temporal correlation can also include temporally correlated samples of the same dynamics D1 and D2, as indicated by the smaller dashed arrows.

[0124] Fig. Figure 2E shows a schematic representation of temporally distinct sequences of two dynamics D1, D1'; D2, D2', which comprise a multitude of samples S11, S12, S12', S21, S22', acquired by the field probe array at different spatial positions X1, X2. For clarity, only one sample S21 of the first dynamic D1, D1' at a second spatial position X2 and only one sample S12', S22' of the second dynamic D2, D2' at the first and second spatial positions X1, X2, respectively, are shown in the acquired samples. However, both dynamics D1, D1'; D2, D2' also comprise a multitude of samples S11, S12, S21, S12', S22' at different spatial positions X1, X2.

[0125] Each dynamic D1, D1'; D2, D2' was recorded over a time interval I1, I2, specifically synchronized with the electromagnetic actuation of the MRI machine, as in Fig. 2A described. Fig. Figure 2E further shows exemplary correlations between the samples S11, S12, S12', S21, S22' and the dynamics D1, D1'; D2, D2'. The spatiotemporal correlations are indicated by dashed arrows between the samples S11, S12, S12', S21, S22' and the dynamics D1, D1'; D2, D2'. The spatiotemporal correlations, i.e., with one temporal and one spatial degree of freedom, are represented by solid arrows between the samples S11, S12, S12', S21, S22' and the dynamics D1, D1'; D2, D2'.

[0126] Even sets of samples of a dynamic range D1, D1', which were recorded at different spatial positions X1, X2, but in the same time interval I1, can be the subject of a temporal correlation, since individual samples S11, S12, S21 of this dynamic range D1, D1' can be correlated in a temporal area.

[0127] Fig. 2E further shows, similarly to in Fig. 2A_3, inconsistent field estimates based on the dynamics D1, D1'; D2, D2'. Due to the different spatial positions X1, X2 of the field probes of the field probe array, the field estimates can differ to some extent, e.g., because they are spatially separated or affected differently by noise. However, the magnetic field at the different spatial positions X1, X2 is highly correlated in both a spatial and a temporal degree of freedom. Therefore, a time-specific, a space-specific, and / or a spatiotemporal correlation can contribute significantly to the measurement noise and must be minimized. For example, spatiotemporally correlated noise, such as local magnetic field distortion, e.g., due to coil heating or patient movement that shifts spatially over time, can only be adequately accounted for by considering a spatiotemporal correlation.Even if in . Fig. Where only two different spatial positions X1, X2 are represented in Figure 2E, these dynamics D1, D1'; D2, D2' are preferably captured at a multitude of different spatial positions X1, X2, in particular at more than 10, as shown in Figure 2E. Fig. 1 schematically represented.

[0128] The spatiotemporal field evolution in an MRI system is expected to exhibit significantly lower dimensionality than the typical projection approach for field estimation. Furthermore, a strong correlation between temporal and spatial behavior is expected to be induced by the sequence and activation, as well as by external sources.

[0129] Fig. Figure 3 shows a schematic block diagram and corresponding diagrams illustrating a spatiotemporal magnetic field generation and estimation based on spatially localized measured values.

[0130] Fig. Figure 3 illustrates a spatially and temporally dependent field development in step 33, which is influenced by a sequence of step 31, a field activation of step 32 and field drift / external fields of step 34.

[0131] The graph G1 of Fig. 3 shows a magnetic field K G (t',t) of the sequence step 31 in the time range t including the repetition time TR.

[0132] The diagram G2 in Fig. Figure 3 shows a generalized transfer function GTF of the field actuation of step 32 in a frequency range f.

[0133] The diagram G3 in Fig. Figure 3 shows a cross-correlation of level 33 in the spatial and temporal domain as a three-dimensional diagram K. B (r',r,t',t).

[0134] Diagram G4 shows the magnetic field B(f) due to field drifts / external fields from step 34, i.e., noise in the frequency domain f. The field development 33 is generated by a multitude of field probes 21–27 (see Fig. 1) measured locally, so that in step 35 a large number of local field measurements B rp (t) can be obtained for p = 1, ..., n. Based on these local field measurements B rp (t) can be used in step 36 to obtain a spatially and temporally correlated field estimate B̂ (r,t, B rp (t)) can be determined, e.g. by estimation using a limited basis set of spherical harmonic functions.

[0135] By including the previously described spatial-temporal correlations of different sample values / dynamics(s) and / or correlations between different dynamics, the noise in the estimation of the field development 36 can be significantly reduced.

[0136] Signal correlations for noise reduction in field estimation can be determined by calibrating, calculating, or estimating information about the sequence or the field triggering system. A proven method for measuring the characteristics of the field triggering system is to measure its transfer or impulse response function. Similar approaches can be used to estimate a transfer function during the actual measurement. Sequence information can be gathered from the MRI scanner's control unit or its outputs in the actuation chain.

[0137] It should be noted, however, that most of the noise reduction approaches presented below do not require the actual response function or impulse waveform, but only a statistical expression of their relationships. For sufficiently linear systems, these relationships can be expressed by the cross-correlation / covariance functions of the output values. Information about the absolute timing is therefore not necessary; only the relative timing between the output values ​​is important.

[0138] In cases where signal correlations are not known as described above, they can be implicitly estimated or used by dimensionality-reducing noise reduction algorithms. A standard approach known in the literature is based on singular value decomposition or principal component analysis. More complex variants such as singular spectral analysis or sparse singular value decompositions are also capable of using implicit redundancy for noise reduction and improved data quality.

[0139] Although the target estimate is a (magnetic) field value, in many applications, e.g., when using field measurements for reconstruction, the time integral of the field is used. When using NMR / EPR field probes, this unit relates directly to the phase evolution φ(t) of the RF signal emitted by the field probe: φ(t)=γ∫‖B(t)‖dt.

[0140] Due to the nearly linear relationship between the two quantities, the phase and field signals can be denoised analogously, and the algorithm can often be applied to both input values. However, for optimal estimation, it can be advantageous to explicitly include the temporal / spectral noise statistics of the field probe used. In the case of NMR field probes that operate with coherence (e.g., FID), the RF signal is subject to white Gaussian noise (borderline case of thermal noise). However, if field values ​​are derived, the noise statistics of the resulting field estimate are spectrally weighted by differentiating with a factor ω. If a field probe is used to measure the instantaneous magnetic field or a component thereof (e.g., Hall sensor, atomic magnetometer, EPR, nitrogen vacancy (NV)-based magnetometer, etc.) and the phase signal (e.g.,NMR-based field probes) are integrated, resulting in a noise weighting of. 1ω. Principal component analysis / singular value decomposition approach:

[0141] In this approach, singular value decomposition or principal component analysis is applied to the field probe array measurements. The temporal data from the field probes are divided into time intervals such that long-term correlations are accounted for in the autocorrelation function. In a very typical case, this would mean that the data are arranged in equal time intervals relative to the repetition time TR of the sequence. Brp(tτ)=Brp(tτ+j⋅TR), j=1,...,T where t τ = tj·TR is the relative time within the time interval of the repetition andj enumerates the repetitions.

[0142] In the simplest implementation, the data collected by all field probes and repetition times are stacked in a matrix: S=(Xr1 1(t1)Xr1 1(t2)⋯Xr2 1(t1)Xr2 1(t2)⋯⋯…⋯Xrn 1(t1)Xrn 1(t2)⋯Xr1 2(t1)Xr1 2(t2)⋯⋯⋯⋯Xrn T(t1)Xrn T(t2)⋯)

[0143] Note that the values ​​X can be the magnetic field B or its integral as phase, or k-space coefficients or other projected field or phase expansions in a specific spatial basis set.

[0144] However, it should be noted that the data can also be arranged analogously in more than 2 dimensions in order to consider more than one possible correlation in the time domain.

[0145] The matrix S can then be decomposed using a singular value decomposition (singular value decomposition): S=U∑V*

[0146] In the case of a higher dimensionality of S, corresponding higher-order singular value decompositions can be applied.

[0147] Due to the induced correlations and sparsity described above, the singular values ​​exhibit strong decay properties. Singular values ​​below a certain threshold T can therefore be deleted or filtered to denoise the data. (PT(Σ))q,q={Σq,q for Σq,q>T 0 esle.

[0148] The denoised data can then be read from the inversely transformed matrix: S^=UPT(Σ)V*.

[0149] As already mentioned, the approach would be analogous to the projected field development a n (t) applicable in a given spatial basis set.

[0150] The difference between the two approaches above lies in the weighting of the coefficients. Signal weighting can be introduced in a known manner. Of particular interest is a weighting that reflects the signal and noise propagation of the field interpolation into the volume / region of interest for imaging.

[0151] In a specific implementation, this can be achieved by considering the signal in the ROI for compression: (SROI)c,τ=ΣP+Brp(t)⋅Ψn(rc) Where r c a set of checkpoints within the ROI.

[0152] It is understood that estimates of the noise statistics among the field probes can be incorporated into the estimate in a similar manner as described below.

[0153] As mentioned previously, such an approach takes into account correlations in the spatiotemporal domain. In the prior art, temporal correlations are often calculated separately for each spatial term, neglecting correlations between the spatial terms. Another prior art is the use of singular value decomposition (singular value decomposition / principal component analysis) and the exclusive use of spatial compression, i.e., restricting the basis set for field interpolation and reconstruction to a basis set given by principal component analysis truncation.

[0154] The Fig. Sections 4A - 4G show exemplary graphically represented data illustrating the effect of noise reduction using a principal component analysis algorithm, taking into account spatiotemporal correlations.

[0155] Fig. 4A shows the phase ψ n(t), which is the magnetic phase evolution ψ n (t) corresponds to a multitude of field probes of the field probe arrangement, which includes several, substantially different dynamics of a multi-shot spiral sequence.

[0156] Fig. Figure 4B shows the principal singular vectors PC1(ψn(t)) with the dominant singular values ​​extracted from the phase corresponding to the magnetic field profile of Fig. 4A corresponds to this.

[0157] The Fig. Figures 4C-4E show the singular values ​​of the singular vectors 1-80 in descending order. The singular values ​​decrease rapidly, suggesting that only a few singular vectors can be used to adequately describe the data.

[0158] Fig. 4F exhibits phase evolution noise Δψ n(t) before nominal gradient encoding begins, applying only temporal filters. To better visualize the phase evolution noise, in Fig. 4F subtracts the phase.

[0159] Fig. 4G shows the same phase evolution noise Δψ n (t) like Fig. 4G, but using singular value decomposition. Singular spectral analysis

[0160] The approach of singular spectral analysis (Singular Spectral Analysis) or its multivariate / multichannel versions is procedurally similar to the singular value decomposition approach described above. It is understood that the window width used can be chosen based on the expected temporal correlations induced by the sequence and / or the system's transfer function. Here, too, noise reduction is achieved by truncating the singular value decomposition (Singular Value Decomposition). When singular value decomposition is applied directly to the measured field / phase developments, singular spectral analysis can detect structures within the data without explicitly specifying the repetition time.In such cases, singular spectral analysis is expected to provide stronger noise reduction for spatiotemporal filters and, in principle, even a certain degree of signal extrapolation capability, as reported in various applications in the literature. However, its greatest disadvantage is its higher numerical complexity. Singular spectral analysis is just one example of the ever-increasing number of autoregressive methods. Regulated projection approach

[0161] In another embodiment, the result of the field estimation is regulated towards a known / predefined, multivariate statistical representation of the field evolution. For the sake of simplicity, the following is discussed in the Fourier / spectral domain. The filters can be converted to the time domain or to a representation of the finite impulse response.

[0162] As previously suggested, field development can be expressed by a field extent. The probable field development terms a n (ω) are then, assuming a transfer function H nj (ω) for the field activation of channel j to the basis function Ψ n (r) and an (unknown) sequence of impulses g j (ω) for channel j: αn(ω)=ΣΗnj(ω)gj(ω).

[0163] The expected spectral cross-power is therefore: αn(ω)⋅αn'(ω)*=(Ka(ω))n,n'=∑j,j'Hn,j(ω)gj(ω)(Hn',j'(ω)gj'(ω))*=H(ω)Hg(ω)H(ω)*, where (K g (ω)) j,j' = g j (ω) · g j '(ω)* is the spectral cross-covariance of the sequence.

[0164] If the sequence is unknown, an assumption about the sequence would affect the choice of (K g (ω)) j,j' = δ j,j' This can result in... Even without explicit knowledge of the detailed impulse waveforms and their timing, K g(ω) can be estimated more accurately in various ways, e.g. based on the repetition times of the sequence or the readout properties.

[0165] K a (ω) can then be calculated using a gradient transfer function, as given above. The transfer function can be measured using established methods or calculated from system properties. K a (ω) can also be determined from the measurement itself, since it represents the power in the field development itself.

[0166] The field estimate can then be obtained from the solution of a minimization problem of the following type: argmina(ω)(‖Pa(ω)−Br(ω)‖Q2+λ⋅a*(Ka)+a).

[0167] While + denotes a suitable inverse, the Q-norm of a matrix X is ||X|| Q = X H QX and Q denote an error weighting, such as that caused by the noise covariance of the field measurement B. r(ω) or other (multivariate) mass of the reliability of the probe data is induced. The latter expresses that the error should be weighted and decorrelated according to its noise level. The regularization parameter λ can be chosen according to known criteria and techniques such as L-curve optimization, discrepancy regularization, and others. This minimization problem can be solved by known matrix inversions.

[0168] The resulting multivariate frequency-domain filter can then be applied to Fourier-transformed measurements or transposed into a time-domain representation. Appropriate truncation or fitting to a finite impulse response can further improve the numerical efficiency of the application.

[0169] The Fig. 5A and Fig. Figure 5B shows an exemplary data set of a mean squared error “RMSE” ​​and a maximum error “Max-Fehler” of a magnetic field estimate in a field of view of a field probe arrangement, which was obtained on the basis of a prior art approach by applying a projection and a low-pass filter, referred to as the “standard method”.

[0170] The Fig. 5C and Fig. 5D shows the exemplary dataset of the Fig. 5A and Fig. 5B of the mean squared error “RMSE” ​​and the maximum error “Max error” of a magnetic field estimate in the field of view of the field probe arrangement, which was obtained on the basis of a regularized inversion approach, i.e. taking into account the previously described spatiotemporal correlation, referred to as the “Std-Mah method”.

[0171] The Fig. Figures 5A-5D show that the “Std-Mah method” enables more effective noise reduction for both the “RMSE” ​​and the “Max error”.

[0172] The Fig. 5E and Fig. 5F show a relative change in the signal-to-noise ratio of the previously described approaches of the Fig. 5C and Fig. 5D in relation to the Fig. 5A and Fig. 5C. QUOTES INCLUDED IN THE DESCRIPTION

[0000] This list of documents cited by the applicant was automatically generated and is included solely for the reader's convenience. The list is not part of the German patent or utility model application. The DPMA accepts no liability for any errors or omissions. Cited non-patent literature

[0000] Dubovan, PI, Gilbert, KM, & Baron, CA (2023). A correction algorithm for improved magnetic field monitoring with distal field probes. Magnetic Resonance in Medicine; 90:2242-2260

[0006]

Claims

[1] Computer-implemented method for improving the signal-to-noise ratio of a magnetic field profile for a magnetic resonance imaging device (201), comprising the following steps: - Providing sample values ​​(S11, S21) of a magnetic field (M), which in particular include or consist of gradients of the magnetic field (M), which were recorded at a first respective time at at least two different spatial positions (X1, X2), - Providing sample values ​​(S12', S22'; S12, S22) of the magnetic field (M) which are acquired at a second respective time at at least two different spatial positions (X1, X2), wherein the sample values ​​(S11, S21, S12', S22'; S11, S21, S12, S22) are acquired by a field probe arrangement (101) while the field probe arrangement (101) is located in the magnetic field of an examination volume (V) of the magnetic resonance imaging device (201), - Determining a corrected magnetic field profile (c) with improved signal-to-noise ratio based on a spatiotemporal correlation of the sampled values ​​(S11, S21, S12', S22'; S11, S21, S12, S22), - Providing the corrected magnetic field profile (c) for image reconstruction or gradient system calibration, - Optional reconstruction of the image or generation of the gradient system calibration based on the corrected magnetic field profile and provision of an output that includes the reconstructed image or gradient calibration. [2] Computer-implemented method according to claim 1, wherein the first time point lies in a time interval (I1) containing a first dynamic (D1, D1') with a plurality of samples (S11, S12) of the field probe arrangement (101), and the second time point lies in a time interval (I1; I2) containing a second dynamic (D2, D2') with a plurality of samples (S21, S22; S12'; S22') that differ from the first dynamic (D1, D1'). [3] Computer-implemented method according to claim 1, wherein the first time point is in a dynamics (D1, D1'; D2, D2') comprising a plurality of sample values ​​(S11, S12; S21, S22) of the field probe arrangement (101), and the second time point is in the same dynamics (D1, D1'; D2, D2'). [4] A computer-implemented method according to any of the preceding claims, comprising providing at least one first dynamics (D1, D1') comprising a plurality of samples (S11, S12) and a second dynamics (D2, D2') comprising a plurality of samples (S12'; S21; S22') acquired over different time intervals (I1, I2), wherein the method synchronizes the predetermined time intervals (I1, I2) of the acquisition of the dynamics (D1, D1'; D2, D2') with an operation of the magnetic resonance imaging device, in particular such that at least one parameter that defines or contributes to magnetic field generation is synchronized with the time intervals (I1, I2) of the acquisition of the dynamics (D1, D1'; D2, D2'). [5] Computer-implemented method according to one of the preceding claims, wherein the sampled values ​​(S11, S12; S21; S22') were acquired at at least 3 different spatial positions (X1, X2), in particular at at least 4 different spatial positions (X1, X2), preferably at at least 16 different spatial positions (X1, X2). [6] Computer-implemented method according to any one of the preceding claims, wherein the determination of the corrected magnetic field profile (c) comprises the application of a dimensionality reduction algorithm (2) to the sampled values ​​(S11, S12; S11, S21; S11, S12'; S11, S22') to achieve noise reduction, in particular (i) a principal component analysis, singular value decomposition, or singular spectral analysis algorithm, and / or (ii) a dimensionality reduction algorithm selected from at least one of a locally linear embedding, a singular spectral analysis, a kernel principal component analysis, a kernel principal component analysis, a wavelet-based spectral analysis, a wavelet-based independent principal component analysis, an isometric mapping, a t-distributed stochastic neighbor embedding, uniform manifold approximation and projection, an autoencoder, a machine learning algorithm, Proper Orthogonal Decomposition,Dynamic mode analysis, spatiotemporal autoencoders, spatiotemporal convolutional neural networks, spatiotemporal graph neural networks, nonlinear independent component analysis, spatiotemporal variational autoencoders and / or spatiotemporal cluster analysis. [7] Computer-implemented method according to claim 6, wherein the dimensional reduction by the principal component analysis, singular value decomposition or singular spectral analysis algorithm (2) is selected such that noise suppression of the corrected magnetic field profile (c) is enabled, in particular such that a noise-reduced field development is calculated by specific weighting of singular values, in particular such that only principal components greater than or equal to a threshold value (T) are selected, in particular a threshold value (T) dependent on the sample values ​​(S11, S12; S21; S12'; S22') or a predefined threshold value is selected. [8] Computer-implemented method according to any of the preceding claims, wherein the spatiotemporal correlation is derived on the basis of measured or derived properties of the magnetic resonance imaging device, in particular (i) a linear transfer function and / or a nonlinear transfer function of the magnetic field, (ii) derived system properties of a shim system, and / or (iii) at least one nominal sequence information selected from a nominal gradient timing control, a nominal repetition time, an echo time and a nominal bandwidth. [9] Computer-implemented method according to any of the preceding claims, wherein determining the corrected magnetic field profile (c) comprises: (i) applying a noise reduction filter to the magnetic field profile (c) or to the sampled values ​​(S11, S12; S21; S12'; S22') in the spatiotemporal domain, wherein the filter is preferably selected from at least one of a Wiener filter, a Kalman filter or a convolutional neural network filter and a Savitzky-Golay filter, or (ii) determining the corrected magnetic field profile (c) based on the spatiotemporal correlation is carried out by a supervised or unsupervised machine learning model, in particular a neural network, preferably a convolutional neural network. [10] Computer program product which, when the program is executed by a computer, causes the computer to perform the steps of the computer-implemented method according to any of the preceding claims. [11] Computer-readable storage medium containing the corrected magnetic field profile (c) with improved signal-to-noise ratio based on a spatiotemporal correlation that can be obtained by the computer-implemented method according to any one of claims 1 to 9. [12] System comprising the field probe arrangement (101), in particular a magnetic resonance imaging device (201), and a processing unit (3) configured to carry out the computer-implemented method according to one of claims 1-9. [13] System according to claim 12, wherein the field probes (21, 22) of the field probe arrangement (101) may be NMR or EPR field probes comprising an active medium selected from at least one aqueous solution and at least one lipophilic component, in particular at least in the vicinity of means for NMR or EPR excitation and / or detection, wherein a smallest dimension of an NMR / EPR active region of the active medium is preferably selected from one of the following regions: 0.2 mm - 0.7 mm, 0.7 mm - 1.1 mm, and 1.1 mm - 2 mm. [14] Computer-implemented method for improving the signal-to-noise ratio of a magnetic field profile for a magnetic resonance imaging device (201), in particular according to one of claims 1-9, comprising the steps: - Providing an initial dynamics (D1) comprising a plurality of initial samples (S11, S12) of the magnetic field (M), which in particular include or consist of a gradient of the magnetic field and are distinct from each other, - Providing a second dynamic (D2) comprising several second samples (S11', S12') of the magnetic field that are distinct from one another, wherein the samples (S11, S12, S11', S12') are acquired by a field probe arrangement (101) while the field probe arrangement (101) is located in a magnetic field of an examination volume (V) of the magnetic resonance imaging device (201), wherein the first dynamic (D1) and the second dynamic (D2) are substantially different from one another, and - Determining a corrected magnetic field profile (c) with improved signal-to-noise ratio (SN) based on a temporal correlation of the dynamics (D1, D2). [15] Computer-implemented method according to claim 14, wherein the temporal correlation is at least partially a temporal correlation of a plurality of samples (S11, S12; S11', S12') of the same dynamics (D1; D2). [16] Computer-implemented method according to one of claims 14 or 15, wherein the method comprises acquiring the at least one first dynamics (D1) and the at least one second dynamics (D2) over predetermined time intervals (I1, I2), in particular the same predetermined time intervals (I1) or different time intervals (I1, I2), wherein the method comprises synchronizing the time intervals (I1, I2) of acquiring the dynamics (D1, D2) with an operation of the magnetic resonance imaging device, in particular such that at least one parameter that defines or contributes to magnetic field generation is synchronized with the time intervals (I1, I2) of acquiring the dynamics (D1, D2).

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