Technique for calibrating magnetic resonance imaging data

Abstract

The invention relates to a method and to a device for calibrating magnetic resonance imaging, MRI, data. Additional spatial encoding fields applied in MRI need to be precisely calibrated to ensure accurate spatial encoding. Prior art calibration techniques usually require additional field mapping scans and are time-consuming and not accurate enough. In order to solve these problems, a technique of calibrating magnetic resonance imaging, MRI, data, is provided. The technique comprises providing (S100) first MRI data (10) acquired by a first MRI data collection scan, wherein an object (1) is subjected to a static magnetic field (B0), magnetic gradient fields (ΔB0), and RF coils' fields (B1), generated by an MRI scanner; providing (S200) second MRI data (15) acquired by a second MRI data collection scan, wherein the object (1) is subjected to the static magnetic field (B0), the magnetic gradient fields (∆B0), the RF coils' fields (B1) generated by the MRI scanner (100), and an additional superimposed spatial encoding field (Δ'B) generated by the MRI scanner (100) or an additional field generating hardware component. The technique further comprises calibrating (S300) the additional spatial encoding field, the calibrating comprising: determining spin phase evolution maps (60) resulting from the additional spatial encoding field (Δ'B), from the first and the second MRI data, wherein for multiple time instants, a neighbourhood (20) of ĸ-space data in the first MRI data (10) are interpolated to a ĸ-space data point (30) in the second MRI data (15), or vice versa, by means of a linear equations system in ĸ-space, which is solved by inversion with optional regularization to determine the spin phase evolution maps (60).

Description

[0001] Technique for calibrating magnetic resonance imaging data

[0002] Field of the invention

[0003] The invention relates to a method and to a device for calibrating magnetic resonance imaging, MRI, data.

[0004] Technical background

[0005] In the present specification, reference is made to the prior art references [1] -

[0089] as listed at the end of this specification. The references illustrate technical background of the invention and related prior art techniques.

[0006] Magnetic resonance imaging (MRI), mainly utilizing linear magnetic field (BO) gradients [1-4] and RF (Bl) receivers [5-8] for spatial encoding and image generation, continues to confront challenges due to its inherent slowness, despite significant progress in fast imaging techniques [9- 14,6,7,15,8,16-24] since its invention in 1973 [1], From 1980s, MRI employing linear gradients switching has been theoretically characterized as sampling the objects' Fourier-domain representations, referred to as k-space [25-27], along a trajectory defined by the time integral of the current waveforms in gradient coils. This mathematical framework makes MRI acquisitions visible on a multidimensional Fourier grid, precisely controlled by manipulating the pulse sequence of RF and linear gradients, thereby fostering numerous breakthroughs in rapid scans [10-14] with straightforward interpretability. Subsequently, in the 1990s, advances in NMR phased array [5] enabled exploitation of the spatially distinct sensitivity profiles by multiple RF receivers to resolve aliased pixels in subNyquist sampling [6-8], This approach, called parallel imaging, which samples k-space using a GRAPPA kernel [8] specific to each RF channel rather than a point, further accelerates MRI in both spatial [6-8,16] and temporal

[0017] dimensions given higher information throughput.

[0007] In the subsequent two decades to the present, through optimal integrations of tailored pulse sequences and parallel imaging techniques [18-21,28], coupled with more sophisticated mathematical signal processing [22-24,29-33], there has been a consistent enhancement in both the acceleration factor and reconstruction quality of MRI scans. Meanwhile, alternative efficient imaging methods have been explored [34-60], which diverge from the conventional linear gradients and RF receivers - the two main "spatial encoders" for modern MRI. However, these techniques disrupt the fundamental k-space formalism [25-27,42,44,45,49] and the nonlinear field calibration could be challenging [42,43,54,57,61], resulting in much less understanding and very limited adoption.

[0008] Despite the challenges in surpassing Fourier imaging based on linear gradients, MRI encoded with nonlinear fields (excl. RF receivers' sensitivity) has a long-standing history in research dating back to the 1970s. In 1974, the concept of synthesizing a moving zero-field position (i.e., sensitive point [62,63]) using gradient coil sets emerged to simplify the retrieval of spatial information, although suffering from low acquisition efficiency as it cannot collect information from all spatial locations simultaneously like modern clinical scanners. In 1978 and 1986, RF amplitude (i.e., rotating frame zeugmatography

[0064] ) and phase encoding

[0065] were introduced, which exploits RF transmit field (Bl) to encode spins without rapidly switched linear gradients (BO). In addition to compressing the dynamic range of RF receiver signals [66,67] in 1980s, a quadratic nonlinear field gradient with moving centres was applied for phase encoding steps, producing localized images called Fresnel transform technique around 1990

[0068] , Later, a PERL field [34-36] (i.e., periodic in x and linear in y) was realized to achieve fast imaging by collecting spontaneous train of echoes shifted in time, with limited spatial regions, assuming finite echo length and negligible T2decay.

[0009] Since 2000, with the forward model incorporating all spatial encoding terms became widely-acknowledged through parallel imaging techniques [7,15], which connects MRI encoding with the inverse problems in applied mathematics, more sophisticated encoded scans became straightforward to reconstruct, not only for linear gradients [20,21,28,69,70] but also for nonlinear ones [38,40,42,54,56], Spins can be projected onto non-bijective, curvilinear magnetic field gradient [38,42] and Z2quadratic fields in shifts

[0040] , with optional combination with linear gradients. They can also be driven by RF phase gradient with parallel transmission systems

[0071] , and employing spin echo (i.e., TRASE [72,73]) to amplify the modulation effect. In contrast to previous techniques [68,35,36] relying on complex and specialized analytical solutions, the forward model with numerically described field distribution can be used to reconstruct images efficiently regardless of the complexity of the encoding fields. However, a nonlinear encoding strategy that substantially outperforms linear gradients in practice has not yet come, and its time-domain sampling efficiency in k-space remained difficult to interpret.

[0010] In 2016, stemmed from the developing nonlinear B0 fields, a technique called FRONSAC (i.e., Fast rotary nonlinear spatial acquisition) started to appear very similar to the linear gradient acceleration methods sampling Cartesian k-space grid with wave-like trajectory (i.e., sinusoidal currents in gradient), such as bunched phase encoding

[0018] and wave-CAIPI

[0069] , However, applying sinusoidal modulation to a second- or third-order magnetic field, FRONSAC samples k-space with a "stamp" instead of a point as by linear gradient (here, neglecting RF sensitivity), which can rotate, grow or shrink when traversing k-space. This dynamic "stamp" shows acceleration potentials with larger k- space coverage per unit-time

[0043] similar to the ones by rapid modulations of linear gradients, but the sampling efficiency of a particular "stamp" was difficult to rigorously quantify in acquisition time-domain. To investigate this emerging direction, an 8-channel local BO coil array [56,59] has been developed as a more general approach for image acceleration, which produces rapid modulation of localized magnetic fields rather than global [38,54], and thus can flexibly synthesize various nonlinear BO fields (incl. linear gradients

[0018] ) to explore the optimal spatial-temporal modulations.

[0011] To overcome theoretical difficulties for nonlinear gradients and make k-space sampling efficiency "visible" again, a mathematical framework for parallel imaging based on reproducing kernel Hilbert space (RKHS) has been extended

[0074] , to produce quantitative k-space efficiency maps where distinct modulation schemes can be rigorously compared at arbitrary acquisition time

[0059] , So far, for 2D Cartesian scans in transverse plane, the optimal modulation BO field for acceleration turns out to be a linear gradient along phase encoding dimension, as the only undersampled dimension that can be naturally reached by simply a zig-zag trajectory similar to bunched phase encoding

[0018] ,

[0012] Notwithstanding these advances in MRI techniques, in particular regarding the capability of generating more advanced spatial encoding fields to encode spins more efficiently, the induced spin evolution due to these spatial encoding fields must be precisely calibrated to ensure accurate spatial encoding and thus high-quality image reconstruction. Prior art calibration techniques usually require additional field mapping scans for calibrating the additional spatial encoding field to determine the phase evolution maps that may be used for reconstructing images from the sampled k-space data. Such calibration techniques are, however, time-consuming due to the need for additional lengthy field mapping scans, and may not be robust enough to produce accurate spin evolution maps for high-quality image reconstruction.

[0013] For example, the conventional field calibration for wave-CAIPI (i.e., a linear gradient modulation technique for image acceleration) replies on additional reference scans, which cannot be later used to add to the final reconstruction to improve signal-to-noise ratio, SNR. These reference scans usually include 2D single slice projection scans

[0086] in x-y plane to characterize y-axis linear gradient modulation and x-z plane to characterize z-axis linear gradient modulation. Each projection scan is acquired twice with and without the linear gradient modulation. This does not consider imperfections of the linear gradients in three-dimensional space (e.g., nonlinearity, induced eddy currents), whereas our auto-calibration technique directly produces nonlinear field modulation maps in two- or three-dimensions with high-robustness without additional field calibration scans.

[0014] Additionally, optimization programs have been utilized to estimate an optimal set of parameters of linear gradient modulations (e.g., time delay)

[0070] to auto-calibrate the k-space modulation trajectory which best fits the measurement k-space data and the reconstructed image. However, not all degrees of freedom (spatially-varying gradient nonlinearity and eddy currents) can be estimated precisely in the optimization, the algorithm convergence may not always lead to the optimal solution completely eliminating any modulation induced artefacts, and the image reconstruction with iterative optimizations costs longer computation time. On the other hand, our auto-calibration technique eliminates the need for such optimization program estimation of a few field modulation parameters, although they are not incompatible with each other.

[0015] For nonlinear BO fields, an earlier way to calibrate the field modulation [40,87] is to phase encode the entire two- or three-dimensional spatial grid, and play out the sinusoidal modulation or DC current of nonlinear gradients at each phase encoded step as the third or fourth encoding dimension, similar to chemical shift imaging. The field evolution or spin phase evolution maps can be calculated from such acquisition. However, this leads to additional very long scan time, is unhealthy for heating up nonlinear gradients hardware without cooling systems, may require a phantom completely filling the RF coil for measuring magnetic fields in a spatial region larger than the imaged object, and can lead to errors if the nonlinear gradient position shifts relative to the ones measured beforehand. The implementation imperfections such as additional eddy currents resulted from additional phase encoded steps implemented in the calibration sequence, and different eddy currents generated by different gradient waveforms may also influence the calibration accuracy. A journal paper

[0061] using this calibration technique still has apparent artefacts in reconstructed brain scans.

[0016] By way of example, a further known calibration technique for local BO coil array

[0059] , a kind of nonlinear gradients, involves performing several gradient echo scans for field mapping of the additional spatial encoding field, each with one local BO coil element sending a small current blip. The last one (e.g., the 9thscan given a total of 8 channels of local BO coils) is performed without any current in any local BO coil as the baseline. Then, these field mapping scans are subtracted by the baseline one, to get relative phase maps contributed by each local coil's current blip. Current monitoring is conducted and used to calculate the phase accumulation map due to 1A current in unit time in a local BO coil. Then, the ESPIRiT algorithm is used to extrapolate all phase maps to high- resolution grid. Afterwards, an MRI data collection scan is performed with undersampling and with arbitrary additional spatial encoding field. The monitored current and the phase maps in the last step are used to produce spin phase evolution maps in the data collection scan. The spin phase evolution maps are used for reconstructing image from undersampled k-space data with additional spatial encoding field, in a forward model, say data equals A times image. A is an encoding matrix containing the spin phase evolution caused by conventional scanner fields and the additional spatial encoding field. By solving this linear system again, a clean image can be obtained. However, this method does not consider the effects by eddy currents spatially varying in 3D, as well as imperfection of current monitoring, and thus, may lead to reconstruction errors in some scans (e.g., sagittal slices for a 8-channel local BO coil array

[0059] ).

[0017] Another prior art approach uses a field camera to calibrate the linear and nonlinear gradient encoding

[0088] , However, an additional field camera setup is needed, field camera tracking of very high order spatial encoding fields has not been demonstrated, and the spin evolution information cannot be obtained directly from the data.

[0018] Objective of the invention

[0019] It is an objective of the invention to provide an improved technique for calibrating MRI data to overcome the above-mentioned known problems associated with conventional MRI calibration techniques. In particular, it is an object of the invention to provide an improved and more efficient calibration method for MRI data in order to determine the spin phase evolution caused by an additional spatial encoding field and that is applicable to both linear and non-linear field modulations and robust to arbitrary scan orientations or volumes in three spatial dimensions.

[0020] Summary of the invention

[0021] These objectives are solved by a method and / or a device comprising the features of the independent claims. Advantageous embodiments and applications of the invention are defined in the dependent claims.

[0022] According to a first general aspect of the invention, the above objective is solved by a method of calibrating magnetic resonance imaging, MRI, data. The method comprises the step of providing first MRI data acquired by a first MRI data collection scan, wherein an object, e.g. a human subject, is subjected to a static magnetic field, BO, to magnetic gradient fields, ABO, and to RF coils' fields, Bl, generated by an MRI scanner. The method further comprises the step of providing second MRI data acquired by a second MRI data collection scan, wherein the object is subjected to the static magnetic field, BO, to the magnetic gradient fields ABO, to the RF coils' fields Bl generated by the MRI scanner, and to an additional superimposed spatial encoding field, A'B. The MRI scanner or an additional field generating hardware component may generate the additional superimposed spatial encoding field. The spatial-temporal ABO pattern applied during the first and the second MRI data collection scan may be identical.

[0023] The method further comprises the step of calibrating the additional spatial encoding field. The calibrating comprises the step of determining spin phase evolution maps resulting from the additional spatial encoding field, A'B, from the first and the second MRI data, wherein for multiple sampling time instants, a neighbourhood of k-space data in the first MRI data are interpolated to a k-space data point in the second MRI data, or vice versa, by means of a linear equations system in k-space. The linear equations system is solved by inversion to determine the spin phase evolution maps. Here, a spin phase evolution map describes spatially varying spin phase accumulation evolved in different MRI sampling time instants. The determined spin phase evolution map thus allows for calibrating the additional spatial encoding field to ensure accurate knowledge of spatial encoding fields for high-quality image reconstruction.

[0024] The term "vice versa" above means that, for multiple time instants, either a neighbourhood of k- space data in the first MRI data are interpolated to a k-space data point in the second MRI data, or a neighbourhood of k-space data in the second MRI data are interpolated to a k-space data point in the first MRI data, by means of a linear equations system in k-space. This interpolation may also be more broadly described as a mapping of a neighbourhood of k-space data in one of the first and second MRI data to a k-space data point in the other one of the first and second MRI data. For example, if there is an undersampling pattern in the second MRI data, the interpolation can exclude the undersampled k-space locations (i.e. zeros in the Fourier grid).

[0025] The linear equations system in k-space may be solved by inversion with optional regularization, which includes linear inversion and regularized inversion.

[0026] The proposed calibration technique advantageously establishes and solves a linear equation system for interpolating a k-space data point in one of the first and second MRI data, from a neighbourhood (patch) of k-space data in the other one of the first and second MRI data to determine the calibration information. The proposed calibration technique requires thus only two data collection scans in contrast to conventional methods estimating additional spatial encoding field, which require ad- ditional reference scans that only produce calibrated field map to certain degree of accuracy and cannot always be used later to add to the final reconstruction to improve SNR as the autocalibration technique proposed here.

[0027] By contrast and according to a further aspect of the invention, the first MRI data and the second MRI data may be both used as imaging data for reconstructing the object image. Therefore, according to a further preferred embodiment, no other field mapping scans additional to the first and second MRI data collection scans are performed for determining the spin phase evolution maps caused by the additional spatial encoding field. In other words, the spin phase evolutions maps are determined only based on the first and second MRI data for imaging purposes. The calibrating as proposed herein is thus very fast and may also referred to as an auto-calibration method as calibration data is acquired simultaneously with the imaging data.

[0028] According to a further aspect, the linear equation system may comprise interpolation kernels as unknowns to be solved, as each kernel determining interpolation coefficients for interpolating a neighbourhood of k-space data in first MRI data to a respective k-space data point in the second MRI data, or vice versa. Preferably, the interpolation coefficients may correspond to the effects by a distinct k-space sampling kernel as the Fourier transform of a spatially-varying spin phase evolution map at one- or multiple-time instants. Each kernel can dynamically change along the acquisition time-domain.

[0029] The interpolation kernels preferably are shift-invariant for a selection of different time instants along the MRI sampling time axis ts, including time axis for readout, multiple phase encoding steps and imaging frames, when the object undergoes identical spatially-varying spin phase evolution (spin phase accumulation) due to the additional spatial encoding field, A'B. Advantageously, the required computations can be substantially reduced by avoiding the estimation of independent kernels among all time points. According to a further aspect, the interpolation kernels for each time instant may be shift-invariant across all RF receiver channels.

[0030] According to a further aspect of the invention, localized cardinal functions may be used as the interpolation weights for interpolating the neighbourhoods of k-space data in the first MRI data to a respective k-space data point in the second MRI data, or vice versa. Preferably, the interpolation kernels mentioned above are defined by the localized cardinal functions. Using the cardinal functions as the interpolation weights and / or the kernels, thus to represent the k-space effects by the induced image-space phase evolution, enables a particularly fast and efficient calibration approach. As noted above, a mathematical framework based on reproducing kernel Hilbert space (RKHS) has been proposed as a technique for processing MRI data, e.g. in the context of parallel imaging

[0074] and nonlinear BO fields

[0059] , to produce quantitative k-space efficiency maps where distinct modulation schemes can be rigorously compared at arbitrary acquisition time

[0059] , Cardinal functions are a set of mathematical functions used as part of the RKHS framework as interpolation weights (and in interpolation theory, signal processing and image reconstruction in general), as will be described later in more detail.

[0031] According yet another aspect, the additional spatial encoding field may comprise spatially-tempor- ally arbitrary magnetic fields, including linear and / or nonlinear fields in arbitrary time-domain modulations. It is therefore a particular advantage of the present calibration technique that it can be efficiently applied to non-linear spatial encoding fields, or linear spatial encoding fields with spatially varying imperfections such as nonlinearity and induced eddy currents. By way of example, the spatial encoding field may be driven by a periodic time-domain modulation signal, for example, a sinusoidal modulation signal. Preferably, the modulation period of the periodic modulation signal is set as a multiple integer of the MRI scanner dwell time for synchronization in timing. This substantially reduces computation time by avoiding separately estimating each kernel out of a large number of kernels among all data points along readout time-axis.

[0032] The first MRI data collection scan may also be referred to as a pre-scan or as a reference scan, and may be used for parallel imaging calibration as well. A resolution of the first MRI data may be lower, e.g. much lower, than a resolution of a final object image reconstructed by using the calibrating of the additional spatial encoding field. However, the resolution of the first MRI data collection scan may also be equal or higher than a resolution of a final object image.

[0033] Additionally or alternatively, the second MRI data may be undersampled with less acquisition time compared to a fully sampled k-space data without the additional spatial encoding field. Advantageously, the MRI data collection scans which self-contains necessary data for auto-calibration can be substantially speed up.

[0034] According to a further aspect, a k-space neighbourhood of the first MRI data or second MRI data may represent a selected subset of acquired data points in the Fourier domain of the object image, centred around the k-space location at the acquisition time, ts. Instead of the term "k-space neighbourhood", the term k-space local region or k-space patch or k-space stamp may be used. According to a second general aspect of the invention, the above objective is solved by a method of magnetic resonance imaging, MRI, an object e.g. a human subject. The method comprises the steps of providing an MRI scanner; acquiring first MRI data by a first MRI data collection scan, wherein an object is subjected to a static magnetic field, BO, to magnetic field gradients, ABO, and to RF coil fields, Bl, generated by the MRI scanner. The method further comprises acquiring second MRI data by a second MRI data collection scan, wherein the object is subjected to BO, to ABO, to Bl generated by the MRI scanner and an additional superimposed spatial encoding field, A'B, generated by the MRI scanner or an additional field generating hardware component. The method further comprises calibrating the MRI data. The calibrating is performed according to a method according to the first general aspect.

[0035] According to a further aspect, the MRI scanner may additionally comprise at least one local magnetic field coil being arranged adjacent to the object for generating the additional spatial encoding field.

[0036] A further general subject of the invention is a computer program product, comprising a sequence of machine instructions, which causes a computer performing a method according to any one of the above-mentioned aspects, when executing the sequence of machine instructions.

[0037] Another general subject of the invention is a medium on which an embodiment of the just mentioned computer program product is stored. The medium (e.g., non-transitory storage medium) may be magnetic (e.g., a floppy disk or a hard drive) or optical (e.g., a compact disk read only memory, or "CD ROM"), and may be read only or random access. If the computer program product is transmitted from a website, server, or other remote source using a physical cable, digital subscriber line (DSL), or wireless technologies then the physical cable, DSL, or wireless technologies such as infrared, radio, and microwave are included in the definition of medium.

[0038] A further general subject of the invention relates to a medium on which an embodiment of the above-mentioned computer program product is stored and which is processable by the computer. Therefore, the computer may be configured to perform arithmetical, logical, and input / output operations, according to the machine instructions encoded in the computer program product. The computer may be configured to only process the imaging data acquired by any MRI scanner, or, according to another aspect, the computer is formed as a control device for an MRI scanning unit, i.e. the computer is directly coupled to an MRI scanning unit. Another general subject of the inven- tion is an MRI scanner comprising a control device, which is configured to perform a method according to any of the above-mentioned aspects.

[0039] Brief description of the drawings

[0040] Further details and advantages of the invention are described in the following with reference to the attached drawings, which show in:

[0041] Figure 1: a flowchart illustrating a method for calibrating MRI data according to an embodiment of the invention;

[0042] Figure 2: an illustration of interpolating a neighbourhood of k-space data in the first MRI data to a k-space data point in the second MRI data according to an embodiment of the invention;

[0043] Figure B: an illustration of solving the linear equation system to obtain localized cardinal functions according to an embodiment of the invention;

[0044] Figure 4: an illustration producing the spin phase evolution maps based on the solved linear equation systems according to an embodiment of the invention;

[0045] Figure 5: a flowchart illustrating a method for calibrating MRI data according to a further embodiment of the invention;

[0046] Figure 6: a flowchart illustrating a method for calibrating MRI data according to a further embodiment of the invention;

[0047] Figure 7 a comparison of reconstructed MRI images with and without the proposed calibration method;

[0048] Figure 8A an MRI device according to an embodiment of the invention; and

[0049] Figure 8B a magnetic field modulation source device included in an MRI device according to an embodiment of the invention.

[0050] Detailed description of preferred embodiments of the invention

[0051] The embodiments shown in the figures correspond, at least in part, so that similar or identical components are labelled with the same reference numerals and reference is also made to the description of the other embodiments or figures for their explanation in order to avoid repetitions. Furthermore, for reasons of clarity, not all (identical) components appearing more than once have always been referenced separately. Theoretical background and mathematical frameworks used for the proposed calibration technique:

[0052] As noted above, a mathematical framework based on reproducing kernel Hilbert space (RKHS) has been proposed as a technique for processing MRI data, e.g. in the context of parallel imaging

[0074] and nonlinear BO fields

[0059] , to produce quantitative k-space efficiency maps where distinct spa- tially-temporally varying modulation schemes can be rigorously compared at arbitrary acquisition time

[0059] , The novelty of the proposed auto-calibration method can be understood in the theoretical background of the RKHS formalism [59,74], which describes general interpolations between distinct k-space data sampling schemes.

[0053] Thus, a theoretical description, for how MRI signal encoding can be mathematically treated and eventually leading to the calibration method as described in this specification, is briefly summarized before. It serves as a background describing how mathematical operations in the proposed calibration method work in accordance with different embodiments:

[0054] In continuous space, the presence of the additional spatial encoding field (e.g., here, taking a general example of arbitrary field generating hardware - local BO coil array) results in another spatial- temporal phase evolution term, on the top of the conventional Fourier and RF sensitivity encoding operator for MRI acquisition. For simplicity, neglecting spin relaxation effects, the acquired timedomain continuous signals obtained by the nthRF receiver coil at the time instant t can be written as: dx] }}dr, (1) with k(t) = YJQ g(r)dr as the k-space trajectory term (i.e., in rad / m) where y is the gyromagnetic ratio (i.e., in rad / s / T), r is the spin spatial location, p(r) is the object spin density, cn(r) is the nthRF sensitivity distribution, g(x) is the shaped pulse of the linear gradients, B (r) is the Bofield distribution produced by unit current in the Athlocal Bocoil, IA(T) is the programmable current waveform in the Athlocal coil.

[0055] Then, the discrete counterpart for MRI sampled data is:

[0056] Sn[t,ky,kz] = fff cn[x,y,z]p[x,y,z]exp{ - ^l{kx[t]x + kyy + kzz + y ZA[BA[x,y,z] Mdx]}} dxdydz, (2) where x, y and z are the three-dimensional spatial coordinates, kx[t],ky,kzare the k-space terms at discrete time instant along one of the three orthogonal dimensions, B [x,y,z] is the spatially varying Bofield produced by the Athlocal Bocoil in finite resolution, I [T] is the current waveform in the Athlocal Bocoil with finite samples.

[0057] Next, in general signal encoding model

[0015] , the discretized MRI acquisition (2) can be described by a linear equations system:

[0058] S = Ep, (3) where S e CNtX1denotes the received time domain signals from all RF receivers, E e CNtXNp denotes the encoding operator considering all "spatial encoders" (e.g., linear gradients, RF receivers and nonlinear gradients), and p e CNPX1denotes the spin distribution for all spatial locations. Nt, Npdenote the total number of acquired time points and pixels, respectively.

[0059] Further, the RKHS framework

[0074] incorporating the nonlinear fields encoding

[0059] further extends the inverse problem formalism considering a signal encoding matrix as in Eq.3, into general interpolations between two arbitrary encoding functions (or matrix) in RKHS, where the Frobenius norm of the interpolation weights, called the cardinal function, relates to the stability of the interpolation, and represents noise amplification as a function of time by the sampling operator.

[0060] MU = R, (4) where Et i,E{ j are both the tested encoding matrix, and E^kis a reference encoding matrix, for evaluating the kernel. The T,N are the total sampling time points and number of RF receivers, with upper dot indicates being for the reference matrix. The noise amplification factor is obtained by taking the Frobenius norm of U along the dimension of t and i (i.e., taking square for each element in U, summing along the vertical dimension, and taking the square root). The asterisk * denotes the conjugate transpose operation.

[0061] Calculated from the cardinal function, the power function quantifies the point-wise bounds of timedomain approximation errors due to interpolating the tested sampling function (or encoding matrix) into the reference one: Therefore, the relative (e.g., compared to fully sampled k-space) time-domain sampling efficiency by all "spatial encoders" can be analytically computed to rigorously compare various nonlinear field encoding, as demonstrated in reference

[0059] ,

[0062] The relation between the RKHS framework and a widely spread parallel imaging technique - generalized autocalibrating partial parallel acquisitions (GRAPPA [8]) - was mentioned by Eqn. (28-31)

[0074] , The GRAPPA reconstruction algorithm, well-known for its robustness, can be reformulated as function approximation in a RKHS, interpolating k-space signal fk(t) with the kthRF receiver, from undersampled data f, (t) with the ithRF receiver, given a total of N RF receiver channels. where Stis a k-space neighbourhood region centred around the sampling location t used for reconstruction, which serves as a finite-width kernel support consisting of GRAPPA weights w^t) as cardinal functions for local k-space interpolation in parallel imaging, instead of using the optimal kernel considering interpolation in the entire k-space grid.

[0063] The weights can be estimated by least square fit, specifically, solving a linear equations system describing how a neighbourhood of k-space data are interpolated via cardinal functions to a data point. This can be implemented by sliding a finite mathematical window through the k-space calibration region C (e.g., a small fully-sampled k-space central region), taking each k-space patch of data at a moving location t; as a row of a calibration matrix A (i.e. each row: Atsii= fi(ts + At)) with distance vector At = t — t. Correspondingly, a data point being interpolated given the moving location t; of the mathematical sliding window (e.g., the mathematical sliding window may define the range a portion of data are selected from, at a moving location at a time) can be taken as a row of another calibration matrix A (special case, a vector) (i.e., each row: Ats i= fk(t;)). Thus, the GRAPPA weights can be obtained: Equivalently, in the RKHS formalism, a kernel matrix M = AA can be formulated by preconditioning of the linear system in (9) by multiplying with A

[0089] , according to the Eqn.(14) in reference

[0059] :

[0064] The kernel matrix is related to an estimate of a truncated covariance function given by:

[0065] In this specification, as described below and as illustrated in Figures 1 and 2, the essential idea of GRAPPA is further extended into (auto-)calibrating arbitrary spatial encoding field (e.g., linear and nonlinear gradient modulations), by adapting the ways to establish linear equation sets from reference scans and thus estimating the preferably a set of various shift-invariant kernels resulting from rapid magnetic fields modulation from selected subsets of data points at distinct time instants, instead of estimating RF receivers' sensitivity as in parallel imaging.

[0066] According to Figure 1, the method of the invention comprises the step S100 of providing first MRI data acquired by a first MRI data collection scan, wherein an object is subjected to a static magnetic field, BO), to magnetic gradient fields ABO, and to RF coils' fields Bl, generated by an MRI scanner. The method further comprises the step S200 of providing second MRI data acquired by a second MRI data collection scan, wherein the object is subjected to BO, ABO and Bl generated by the MRI scanner and to an additional superimposed spatial encoding field A'B generated by the MRI scanner or an additional field generating hardware component.

[0067] Here, a conventional MRI scanner as known in the art may be used for the data collection scans. By way of example only, an MRI scanner similar the one as described in

[0059] may be used. The MRI scanner may additionally comprise an 8-channel local BO coil array consisting of 8 square loops, each in 10cm x 10cm with 14 turn (~41 pH measured at 10kHz) accommodating a 16-transeive-32- receive RF array

[0075] , As illustrated in figures of reference

[0059] , with the power amplifier, the highspeed signal processor, the RF coils and safety evaluations, eventually, ex-vivo and in-vivo Cartesian scans accelerated by rapid BO modulations are carried out within a 9.4T human MR scanner.

[0068] The first MRI data collection scan and the second MRI data collection scans (hereinafter also referred to as reference scans) may be low-resolution scans and / or undersampled MRI scans, e.g. using gradient echo imaging sequence. The spatial-temporal ABO pattern applied during the first and the second MRI data collection scan may be identical.

[0069] By way of example only, a low-resolution MRI scan may be acquired as the first MRI data collection scan with fully sampled k-space data. For the additional spatial encoding field of the second MRI data collection scan, sinusoidal modulations may be used. The second MRI data collection scan may be performed with undersampled k-space location with additionally a small fully sampled region in the k-space centre. The first MRI data collection scan may also comprise a spiral, radial or EPI (Echo Planar Imaging) trajectory scan. In this case, the second MRI data collection scan may be performed using a similar trajectory.

[0070] The method further comprises the step of calibrating S300 the additional spatial encoding field. The calibrating comprises determining, from the first and the second MRI data, spin phase evolution maps resulting from the additional spatial encoding field, A'B, wherein for multiple time instants, a neighbourhood of k-space data in the first MRI data are interpolated to a k-space data point in the second MRI data, or vice versa, by means of a linear equations system in k-space, which is solved by inversion with optional regularization to determine the spin phase evolution maps.

[0071] The calibrated data may be utilized to reconstruct the object image based on the determined spin phase evolution maps, as illustrated by the optional step S400. By way of example only, the calibrated data may be utilized to reconstruct the object image from high-resolution under-sampled k- space locations with the additional spatial encoding fields. The fully sampled k-space lines with additional spatial encoding fields (second MRI data) can also be reconstructed to original k-space data without effects of additional spatial encoding fields. The low-resolution fully sampled k-space data in first MRI collection scan, the reconstructed data using calibration data in the second MRI collection scan including from under-sampled region and fully sampled central k-space region, may be summed up to into one dataset and transformed into image-space for improved SNR.

[0072] It is thus a particular advantage of the proposed calibration technique that these first MRI data and the second MRI data and / or the reference scans may also be thus summed up to one dataset and transformed into image space to be an image with improved SNR and do not cost additional scan time in this sense.

[0073] Fig. 2 to 4 illustrate the determining of the spin phase evolution maps according to a preferred embodiment of the invention. According to the embodiment described in Fig. 2 to 4, the spatial encoding field is driven by a periodic time-domain modulation signal, in particular a sinusoidal modulation signal. However, the proposed method can be applied to any spatial encoding field, including linear and / or nonlinear fields in arbitrary time-domain modulations. Thus the calibration method described here is not only useful for nonlinear gradients modulations but can also applied to conventional acceleration technique involving linear gradient modulations, including using scanner gradient or additional linear gradient insert.

[0074] As illustrated in Fig. 2 in an exemplary manner for two or multiple RF receivers, for multiple time instants, a neighbourhood 20 of k-space data in the first MRI data 10 are interpolated (using an interpolation kernel 40) to a k-space data point 30 in the second MRI data 15. So are the k-space data 20 at other time instants and RF receiver channels. The neighbourhoods 20 of k-space data shown for different time instants and RF receiver channels are described here with the same reference numerals 20. The same applies to the k-space data points 30 and interpolation kernels 40 shown for different time instants and RF receiver channels.

[0075] This interpolation is carried out by means of a linear equations system in k-space, which is solved by inversion with optional regularization to determine the spin phase evolution maps 60.

[0076] From the convolution theorem, the additional phase modulation by arbitrary gradient modulations corresponds to the convolution of its Fourier transform term with the object's k-space representation, leading to sampling the sum signal of k-space data collected by a dynamic "stamp" at a time instant

[0043] ,

[0077] Therefore, assuming finite width of the dynamic "stamp", MRI acquired samples in time-domain tscan be seen as the sum signal of a neighbourhood 20 of k-space data centred around t; without additional nonlinear gradient modulations multiplied by a localized interpolation kernel related to the sampling "stamp". Here, at each phase of sinusoidal modulation, the localized interpolation kernel (also referred to as kernel) should remain identical. Namely, by shifting along phase encoding dimensions in ky(or t_phase,y) and kz(or t_phase,z) within the first and second MRI data 10, 15 (i.e., calibration region), redundant linear equations with the same unknown as the localized cardinal function can be obtained. The shift along the spin phase encoding dimensions y, z is illustrated using the arrows with the reference numeral 41. The time-domain modulation current in linear or nonlinear gradients 21, with the phase #1 or #2 of the sinusoidal modulation cycles shown by white and black circles, is illustrated by the curve at the bottom of Fig. 2. Furthermore, by optionally manually setting the sinusoidal modulation period Tmas multiple integer (L) of the scanner dwell time TADC, every L acquired data point along readout dimension x should experience the identical signal modulation in three-dimensional spatial domains, assuming high-stability of the current produced by power amplifiers. Thus, a linear system for estimating the localized kernel can be established as in Figure 2, by shifting the local interpolation between RF receiver channels, phase encoding dimension with identical spatially varying signal modulation, and between different readout locations (kx) where the phase of sinusoidal modulation remains the same. The latter substantially reduce the computation to avoid separately estimating kernels among all readout points assuming all of them are independent.

[0078] Summarizing the above, the linear equation system comprises interpolation kernels as unknowns to be solved, as each kernel determining interpolation coefficients for interpolating a neighbourhood of k-space data 20 in first MRI data 10 to a respective k-space data point 30 in the second MRI data 15, or vice versa. The interpolation kernels are preferably shift-invariant within a selection of different time instants along the sampling time axis (ts), such as along the readout time axis (t_read,x in Fig. 2), along multiple phase encoding steps (t_phase,y and t_phase,z in Fig. 2), multiple RF receiver channels, or multiple imaging frames, when the object undergoes identical spatially- varying spin phase evolution due to the additional spatial encoding field, A'B.

[0079] As a general remark, it is noted that in the special case of a non-linear spatial encoding field, the conventional k-space formalism doesn't exist strictly speaking, and the acquisition can be seen as sampling the sum value of the elementwise multiplication between the Fourier transform of a spatially-varying signal modulation pattern and the subset of k-space data. In this specification, the k- space formalism and "k-space location" is used nevertheless because it is commonly used in the relevant literature and because the mapping is seen in the Fourier domain of the image usually called k-space, and because the signal processing of the k-space neighbourhood can be convenient in the Fourier domain. The acquired data samples from RF receivers in MRI data collection scans may be first re-gridded to a k-space grid neglecting the presence of additional spatial encoding fields before further processing. By way of example, "tx" is used for the k-space location to indicate that, the k-space is not conventional, and using time notation "tx" instead of "kx" is more appropriate to describe it, although "kx" is also a function of time corresponding to the time integral of linear gradient waveform. The mapping may be seen in the other transform domain instead of Fourier domain, and the resulted data is not k-space strictly speaking. In view of the above, instead of k- space data, the k-space data could also be referred to as "time-domain acquisition data" instead for generality. As illustrated by Fig. 2, first, the linear mapping relationships (linear equation system) is defined that is governing how the additional spatial encoding field, here as an example a spatial encoding field that is driven by a sinusoidal modulation signal, affects the time-domain (i.e., k-space) acquisition data.

[0080] The linear equations relationships are defined at the sampling time location tj corresponding to the Ithphase of the sinusoidal oscillation cycle along the readout time axis, for interpolating a neighbourhood 20 of k-space data in the reference scan without spatially-varying signal modulations (i.e., first MRI data 10) (i.e., fi(t[)) to a data point in the reference scan with signal modulations (i.e., second MRI data 15) (i.e., gi(t|)), using a particular cardinal function where t| is the sampling time location at which the data point in the second MRI data 15 is interpolated to, Dtlis the area of sampling time location t| covered by the sampling "stamp" and used for reconstruction, i is the index of RF receiver channel. Note that, interpolation between the two reference scans from the identical ithRF receiver is considered, but theoretically, more general interpolation is possible, such as from all RF receivers to an arbitrarily chosen channel, jointly estimating the spatial modulation effects of RF sensitivity and local Bocoils.

[0081] The cardinal function used for the interpolation at a distinct sinusoidal phase can be estimated by least square fit, from calibration matrix Fts biand vector Gtsbi(i.e., each row of Ftsbi= fi(tsj + Aq), each row of Gtsbi= g, (ts) ) obtained by mathematically sliding a small window through the corresponding calibration region Qi, at location tswith distance vector A t| = t| — tj, and

[0082] Fig. 3 then graphically illustrates the estimation of the cardinal functions 50 that represent the spin phase modulations imposed by the additional spatial encoding field at different phase of the sinusoidal oscillation cycle. In other words, Fig. 3 thus graphically illustrates the mathematical operation of the linear matrix (the linear equation system) at different phases of the sinusoidal oscillation cycle. The cardinal functions representing the k-space effects of the additional spatial encoding field are solved at different phases of the sinusoidal oscillation cycle by solving the linear systems formulated as general signal interpolation within RKHS. Given the calibration matrix Ftbifrom the non-modulated reference scan and calibration vector Gts | jfrom the modulated reference scan, a linear equation relationship can be formed:

[0083] Ftsj,iUtbi= Gtsbi, (14) where Utbicontains the cardinal function for Ithphase of the sinusoidal oscillation cycle, Ftsbiis a matrix where the data in the mathematical sliding window at all time locations and RF receiver index i is reshaped into a row, Gtsbiis a vector where the data being interpolated at time location tsj and RF receiver index i (i can be more than one index if multiple RF receivers are available) is filled in.

[0084] By performing pre-conditioning of Eqn. (14) by multiplying F^biat two sides of the equation, which usually makes linear systems easier to solve, a similar kernel matrix as in Eqn. (5) is obtained as below. The rows of Ftsbiand Gtsbican be seen as special k-space functions with image-space weightings of the spin density distribution, and is compatible under the RKHS framework for computing the generalized interpolations between functions.

[0085] Mts biUtbi= Rtsbi, (15)

[0086] According to the shown embodiment, the cardinal functions 50 are used as the interpolation weights for interpolating the neighbourhoods 20 of k-space data in the first MRI data 10 to a respective k-space data point 30 in the second MRI data 15. Furthermore, the interpolation kernels are defined by the localized cardinal functions 50.

[0087] The cardinal function 50, as the vector Utbiin Eqn. (15) can be solved by Moore-Penrose inverse, inversion with optional regularizations (e.g., truncated singular value decomposition, TSVD), or iterative methods

[0076] , The cardinal function at phase #1 of the sinusoidal modulation cycles are illustrated in Fig. 2 using the solid lines with reference numeral 40. The cardinal function at phase #2 of the sinusoidal modulation cycles are illustrated in Fig. 2 using the dashed lines with reference numeral 40. It is again noted that while same reference numeral 40 is used for the cardinal functions at phase #1 and phase 2, the cardinal functions are different. Applying the above mathematical framework to an illustrative simple example may be as follows:

[0088] A neighbourhood of k-space data in the first MRI data is selected, e.g., in MATLAB notations, if it is two-dimensional (2D), say [1,2;3,4], Its central point is at the readout time ts. This neighbourhood of data is multiplied by a kernel or cardinal function, say [0.1,1; 10, 100]. The elementwise multiplication is done, in this case [1,2;3,4].* [0.1,1; 10, 100] = [0.1,2;30,400]. The sum of the multiplied values is taken, in this case is 0.1+2+30+400 = 432.1. This sum value is the k-space data point being mapped in the second MRI data at the readout time ts. Namely, to estimate the cardinal function is to find kernels with values which satisfy the linear mapping from the neighbourhood data [1,2;3,4] to the data point 432.1. By shifting across different k-space data values at different k-space locations ts and RF receiver channels where the kernel should remain identical, more independent linear equations can be obtained and this kernel as the unknown in linear system can be accurately estimated.

[0089] Fig. 4 then illustrates how the spin phase evolution maps 60 are obtained. As illustrated in Fig. 4, the following steps may be carried out: performing a TSVD algorithm with eigenvector cut-off during inversion, reshaping the cardinal functions 50 into three-dimensional k-space kernels properly, removing readout oversampling, zero-filling and finally applying inverse Fourier transform to obtain the image-space phase evolution maps 60 in 2D or 3D spatial dimensions. Again, the different cardinal functions in the upper and lower part of Fig. 3 (and Fig. 4) are described with the same reference numeral 50.

[0090] Fig. 5 shows a flowchart illustrating a method for calibrating MRI data according to a further embodiment of the invention. To avoid repetitions, the following description of Fig. 5 essentially focuses only on the specifics of this exemplary embodiment, and references the explanations and detailed description of Fig. 1 to Fig. 4 for the calculation of the linear equations and phase evolution maps, which also apply to the embodiment of Fig. 5 - unless explicitly stated otherwise.

[0091] In step S100, first MRI data are provided acquired by a first MRI data collection scan using a conventional static magnetic field, B0, a linear magnetic field gradient, ABO, and RF coil fields, Bl. The first MRI data do not have to be high-resolution MRI data. Only a fully sampled k-space region is needed, such as several (e.g., 40) k-space lines, preferably at the k-space centre, with fully-sampled but low-frequency phase encoded steps. The first MRI data is usually used for parallel imaging calibration in acceleration MRI scans, and in our case, can be re-used for the same purpose of parallel imaging calibration in parallel to our calibration of additional spatially-temporally varying spatial encoding fields.

[0092] In step S200, second MRI data are provided acquired by a second MRI data collection scan, using BO, ABO, and Bl and additionally, the previous magnetic fields are superimposed by a spatial encoding field, arbitrary in spatial and temporal domain. The acquisition with the additional spatial encoding field may be performed as follows: k-space data undersampled by missing some k-space sampling locations are acquired, and preferably a fully sampled k-space central region is additionally acquired (e.g., similarly, 40 k-space readout lines are acquired at fully sampled but low-resolution phase encoded steps).

[0093] The calibrating of the additional spatial encoding field may comprise the following steps S310 to S370 of Fig. 5:

[0094] Step S310 of Fig. 5: in the second MRI data, a sampling point at time ts is located along readout dimension, at time tpl, tp2 along phase encoded dimension, in a RF receiver channel s. The location is denoted (ts, tpl, tp2, s). The notation used here in an exemplary manner is kept more general to account for Cartesian and non-Cartesian MRI sampling trajectories.

[0095] Step S320 of Fig. 5: In the first MRI data, a neighbourhood of (ts,tpl,tp2) is located in all available RF receivers (s=l,2,...), and denoted (ts-tl:ts+tl,tpl-t2:tpl+t2,tp2-t3:tp2+t3, s).

[0096] Step 330 of Fig. 5: A linear mapping relation (a linear equation system) is established between the neighbourhood of k-space data in the first MRI data, and the data point in the second MRI data. Specifically, in the linear equation system formalism y=Ex, where y is a mxl vector, E is a m x n matrix, x is a n x 1 vector, the neighbourhood data at (ts-tl:ts+tl,tpl-t2:tpl+t2,tp2-t3:tp2+t3, all s) is put as a row of E, the data point at (ts,tpl,tp2,s) as a point in y.

[0097] Step 340 of Fig. 5: Iterate the linear mapping relation across a selection of time locations ts, when the additional spatially-varying spin phase accumulation due to additional spatial encoding fields remain identical, to formulate a linear system. Perform this step for different linear mapping relation across another selection of time locations when there is another spatially varying spin phase accumulation due to additional spatial encoding fields, to formulate other linear systems.

[0098] Step S350 of Fig. 5: When iterating over all time locations ts and putting the data from a neighbour- hood-to-point mapping to the linear system denoted as y=Ex, the vertical dimension of E and y becomes sufficiently long so that E becomes well-conditioned. Thus, this linear equation system is inverted with optional regularizations, so that x as the cardinal function for the specific map- ping / phase accumulation map is obtained. It is noted that many linear system inversion methods exist that could be applied to perform the inversion. By way of example only, a truncated singular value decomposition, TSVD, may be used with a threshold truncation in subspace for denoising purposes. Additionally, before inverting y=Ex, the linear system may be preconditioned to be EHy=EHEx, as the equation (14-15) mentioned above is EHE, Utbiis x, and F^ jGtsbiis EHy. This precondition usually makes linear system easier to solve.

[0099] The above operations are iterated to all different cardinal functions, that is, at time locations ts having different phase accumulation maps due to additional spatial encoding field. In the current embodiment, a sinusoidal modulation of a linear or nonlinear BO field is used, setting the sinusoidal oscillation period (e.g., 120us = 40x Bus) as multiple integer of MRI scanner dwell time (e.g., Bus). In this way, for one cardinal function estimation, ts can be shifted to all time instants along readout axis when the sinusoidal waveform reaches the same phase. Advantageously, the estimation can be executed much faster using a computation program in computers.

[0100] As a result, all cardinal functions are acquired.

[0101] Step S360 of Fig. 5: The readout dimension oversampling is eliminated by averaging, e.g. every 8 neighbouring MR samples if 8x oversampling along readout is employed.

[0102] Step 370 of Fig. 5: The cardinal functions are zero-filled and Fourier transformed to image space, to obtain the spin phase evolution maps.

[0103] After step S370 of Fig. 5, the obtained spin phase evolution maps may be used for reconstructing the object image from undersampled as well as fully sampled k-space data with additional spatial encoding field, in a forward model, say data = A x image. A contains spin phase evolution caused by conventional scanner fields and the additional spatial encoding field. By solving this linear system again, a clean image without additional field modulation can be obtained.

[0104] The images obtained directly from the first MRI data (obtained in low-resolution), and reconstructed from undersampled (high-resolution) and fully sampled (low-resolution) data with additional spatial encoding field are summed up properly in the same high-resolution k-space grid to improve the signal-to-noise ratio (SNR) of the final image.

[0105] Fig. 6 shows a flowchart illustrating a method for calibrating MRI data according to a further embodiment of the invention. One of the main differences of this embodiment compared to the embodiment illustrated in Fig. 5 is that a linear mapping relation (linear equation system) is established between a neighbourhood of k-space data in the second MRI data, and a data point in the first data MRI data, and not vice versa as described for Fig. 5. To avoid repetitions, the following description of Fig. 6 essentially focuses only on the specifics of this exemplary embodiment, and references the explanations and detailed description for Fig. 1 to Fig. 4 for the calculation of the linear equations and phase evolution maps which also apply to the embodiment of Fig. 6.

[0106] Step S100 may be identical as described above for the embodiment of Fig. 5.

[0107] In step S200, second MRI data are provided using a second MRI data collection scan, using BO, ABO, Bl, which are additionally superimposed by a spatial encoding field, arbitrary in spatial and temporal domain. The acquisition may be performed as follows: undersampled k-space data for image acceleration scans are acquired, and fully sampled k-space data in a small central k-space region are optionally acquired.

[0108] The calibrating of the additional spatial encoding field may comprise the following steps S310 to S380 of Fig. 6:

[0109] Step S310 of Fig. 6: In the second MRI data, a neighbourhood of (ts,tpl,tp2) is located in all available RF receivers (s=l,2,...) and denoted (ts-tl:ts+tl',tpl-t2:tpl+t2',tp2-t3:tp2+t3', all s). This neighbourhood has undersampled data points as "0" (e.g., [l,0,3;2,0,2,3,0,l]), which can be excluded, and thus only non-zero data are selected as in the patch.

[0110] Step S320 of Fig. 6: In the first MRI data, a sampling point at time ts is located along readout dimension, at time tpl, tp2 along phase encoded dimension, in a RF receiver channel s. The location is denoted (ts,tpl,tp2,s). The location ts is where the patch (neighbourhood) in the second scan is interpolated to, to synthesize missing data due to undersampling. It is noted that ts may not necessarily be the centre location of the patch, depending on the undersampling pattern in k-space. The selection of the location ts with a linear mapping relation synthesizes a missing k-space data loca- tion from a patch (neighbourhood). Different missing k-space locations relative to the patch (neighbourhood) should use different selections of location ts, as different cardinal functions.

[0111] Step 330 of Fig. 6: A linear mapping relation (a linear equation system) is established between a neighbourhood of k-space data in the second MRI data, and a data point in the first MRI data. The relative k-space locations between the neighbourhood and the point should follow the way, how a set of undersampled k-space data with additional spatial encoding field is used to synthesize a missing k-space data at a specific location.

[0112] Specifically, in linear system formalism y=Ex, where y is a mxl vector, E is a mxn matrix, x is a nxl vector, the neighbourhood data at (ts-tl:ts+tl',tpl-t2:tpl+t2',tp2-t3:tp2+t3', all s) is put as a row of E, the data point at (ts,tpl,tp2,s) as a point in y.

[0113] Step S340 of Fig. 6: The linear mapping relation is iterated across all time locations ts, when the additional spin phase accumulation due to additional spatial encoding fields remain identical. When iterating over all time locations ts and putting the data from a neighbourhood-to-point mapping to the general inverse problem formalism y=Ex (y corresponds to Gtsbi, E corresponds to Ftsbi, and x corresponds to Utbiof Equation 14), the vertical dimension of E and y becomes sufficiently long so that E becomes well-conditioned.

[0114] Step S350 of Fig. 6: Subsequently, the linear system is inverted with optional regularizations, so that x as the cardinal function for the specific mapping / phase accumulation map is obtained. It is noted that many linear equation system inversion methods are known to the person skilled in the art that could be used for this purpose. By way of example only, TSVD is used for the inversion with a threshold truncation in subspace. Additionally, before inverting y=Ex, the linear system is preconditioned to be EHy=EHEx, as the equation (14-15) mentioned above: MtsbiUtbi= Rts bi, where Mts biis EHE, Utbiis x, and Rtsbiis EHy. This precondition usually makes linear system easier to solve.

[0115] The above operations are iterated to all different cardinal functions, that is, at time locations ts having different phase accumulation maps due to additional spatial encoding field, with different undersampled k-space relative positions to the patch or selected kernel. By way of example only, in the current embodiment, a sinusoidal modulation of a linear or nonlinear BO field is used, setting the sinusoidal oscillation period (e.g., 120us = 40 x 3us) as multiple integer of MRI scanner dwell time (e.g., 3us) for time synchronization. In this way, for one cardinal function estimation, ts can be shifted to all time instants along readout axis when the sinusoidal waveform reaches the same phase, avoiding estimating a large number of interpolation kernels at all different readout data points separately.

[0116] Advantageously, the estimation can be executed much faster using a computer. As a result, all cardinal functions are acquired.

[0117] Step S380 of Fig. 6: The readout dimension oversampling is not necessarily eliminated according to this embodiment. Preferably, a patch (neighbourhood) size as used in each iteration before, is used to select undersampled k-space data from the second undersampled MRI data subjected to the additional spatial encoding field, multiplied by the estimated cardinal functions, and summed up to a value used to synthesize a particular k-space data point eliminating effects of additional spatial encoding field. The patch (neighbourhood) and the relative location between the patch data and synthesized k-space point preferably should be identical to the corresponding linear mapping relation in each iteration of a cardinal function estimation.

[0118] After step S370, the obtained spin phase evolution maps may be used for reconstructing the object image. By way of example, an image is obtained directly from first MRI data (low-resolution), and reconstructed from undersampled (high-resolution) data with additional spatial encoding field. The overlapped k-space region in both images are averaged in k-space properly and thus, the reconstructions from both data scans summed up to a final image with improved SNR.

[0119] Figure 7 shows a comparison of reconstructed in-vivo MRI images with and without the proposed calibration method.

[0120] Image A of Fig. 7 shows a reference image that has been obtained with no additional spatial encoding fields and with no undersampling. Image B of Fig. 7 shows a reconstructed image subjected to an additional spatial encoding field, based on a 3x3 k-space undersampling. The image has been reconstructed using conventional field mapping scans with current monitors of power amplifiers. Image C of Fig. 7 shows a reconstructed image subjected to an additional spatial encoding field, based on a 3x3 k-space undersampling. The image has been reconstructed using the calibration method as described in this specification.

[0121] The images A to C of Fig. 7 show that the conventional reconstruction method (see image B) can leave apparent residue fold-over effects due to phase estimation errors. However, the image C re- constructed with the calibration technique as described in this specification, which obtained the phase evolution maps directly from a small region of fully sampled k-space reference data with and without BO modulations, produce reconstructed images nearly identical to the reference image. The high robustness of this new calibration technique originates from the data-driven estimation, where a variety of critical factors damaging the accuracy of the estimation of forward model, such as time delay and instability of the power amplifier, eddy currents due to the linear and nonlinear fields (e.g., local BO coils modulation), errors in field mapping scans and mechanical vibrations of field generating coil hardware, are all counted from calculating the cardinal functions representing the overall induced spatially-varying phase evolution effects.

[0122] Figure 8A schematically illustrates an MRI scanner 100 according to an embodiment of the invention. However, it is noted that the proposed calibration method can also be carried out with any other MRI scanner that can generates the magnetic fields BO, ABO, Bl and the additional superimposed spatial encoding field A'B and that is configured to carry out the proposed method.

[0123] The MRI scanner 100 includes an MR scanner unit 110, a control device 120 and a reconstruction device 130, which are configured for implementing the invention. The MR scanner unit 110 includes a main magnetic field device 111, a magnetic gradient device 112, an excitation / acquisition coil device 113 and a magnetic field modulation source device 114. Furthermore, a schematically illustrated holding device 116, like a supporting table, can be provided for supporting an object 1 to be investigated. The components 111 to 114 and 116 are configured as it is known from conventional MR scanners. For example, the excitation / acquisition coil device 113 can comprise a single RF coil or an array of RF coils arranged for parallel MR imaging.

[0124] The magnetic field modulation source device 114 is adapted for creating an additional spatial encoding field, e.g. spatially restricted, time-varying magnetic modulation fields, each covering a spatial section of the object 1. Magnetic field coils 115 of the magnetic field modulation source device 114, e. g. a set of surface coil loop elements, are designed such each magnetic field sufficiently covers the extension of the spatial section of the object to which the modulation is to be applied. Preferably, magnetic field coils 115 are arranged on at least two different sides of the object 1. Examples of the magnetic field modulation source device 114 are described below with reference to Figure 8B.

[0125] The control device 120 includes a main field and gradient control unit 121, an RF pulse control unit 122 and a modulation source control unit 123, each including driving circuits, like excitation and modulation current sources, amplifiers and / or pulse modulators, and at least one computer unit. The components 121 to 123 can be provided with a common computer unit or with separate computer units, coupled with the driving circuits for driving the components 111 to 114. In particular, the modulation source control unit 123 is connected with the magnetic field modulation source device 114 for creating the inventive locally specific frequency modulation of the MR signals. The reconstruction device 130 includes a signal acquisition device 131 coupled with the excitation / ac- quisition coil device 113 and a calculation device 132. Optionally, the calculation device 132 can be coupled, e. g. via direct connection or any other type of data transmission, with the modulation source control unit 123, so that information on the modulation pattern applied to the magnetic field modulation source device 114 can be introduced in the MR image reconstruction. The components 131 and 132 can be provided with a common computer unit or with separate computer units. The computer units of the control device 120 and the reconstruction device 130 are adapted for running software controlling the setting of the components 111 to 114, for collecting and processing MR signals and for MR image reconstruction, resp. In particular, the computer units of the control device 120 and the reconstruction device 130 are configured to carry out the reconstruction method as described in this specification., i.e. to receive the first and second MRI data and to determine the spin phase evolution maps as described above.

[0126] Figure 8B shows an example of a magnetic field modulation source device 114, which comprises 8 independent local magnetic field coils 115 (schematically shown) that are placed in one circular row perpendicular to the z-direction on a hollow cylinder shaped non-conductive carrier (not shown). With a preferred application of the invention, the object 1 to be investigated, for example a head of a human subject, is placed inside this arrangement (as mentioned with reference to the experimental tests below). Each local magnetic field coil 115 is made of e.g. 25 turns of copper wire with a coil diameter of 5 cm to 10 cm. Each coil is independently connected to an individually controllable modulation current source of the modulation source control unit 123 (see Figure 8A) that allows to drive the modulation current in each coil with preselected and independent, different temporal patterns during MR signal collection, e. g. during readout of a FLASH sequence or another sequence. With this embodiment, the magnetic field modulation source device 114 comprises 8 independent local magnetic field coils 115.

[0127] The features of the invention disclosed in the above description, the drawing and the claims can be of significance both individually as well as in combination or sub-combination for the realisation of the invention in its various embodiments. List of cited References:

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Claims

Claims1. Method of calibrating magnetic resonance imaging, MRI, data, comprising the steps of: providing (S100) first MRI data (10) acquired by a first MRI data collection scan, wherein an object (1) is subjected to a static magnetic field (BO), magnetic gradient fields (ABO), and RF coils' fields (Bl), generated by an MRI scanner; providing (S200) second MRI data (15) acquired by a second MRI data collection scan, wherein the object (1) is subjected to the static magnetic field (BO), the magnetic gradient fields (ABO), the RF coils' fields (Bl) generated by the MRI scanner (100), and an additional superimposed spatial encoding field (A'B) generated by the MRI scanner (100) or an additional field generating hardware component; and calibrating (S300) the additional spatial encoding field, the calibrating comprising: determining spin phase evolution maps (60) resulting from the additional spatial encoding field (A'B), from the first and the second MRI data, wherein for multiple sampling time instants, a neighbourhood (20) of k-space data in the first MRI data (10) are interpolated to a k-space data point (30) in the second MRI data (15), or vice versa, by means of a linear equations system in k- space, which is solved by inversion with optional regularization to determine the spin phase evolution maps (60).

2. The method according to claim 1, wherein the linear equation system comprises interpolation kernels as unknowns to be solved, as each kernel determining interpolation coefficients for interpolating a neighbourhood of k-space data (20) in first MRI data (10) to a respective k-space data point (30) in the second MRI data (15), or vice versa.

3. The method according to claim 2, wherein a) the interpolation kernels are shift-invariant for a selection of different time instants along the time axis of signal readout (ts), including multiple phase encoding steps and imaging frames, when the object undergoes identical spatially-varying spin phase evolution due to the additional spatial encoding field (A'B), and / or b) the interpolation kernels for each time instant are shift-invariant across all RF receiver channels.

4. The method according to any one of preceding claims, wherein localized cardinal functions(50) are used as the interpolation weights for interpolating the neighbourhoods (20) of k-space datain the first MRI data (10) to a respective k-space data point (30) in the second MRI data (15), or vice versa.

5. The method according to claim 4, when dependent on claims 2 or 3, the interpolation kernels being defined by the localized cardinal functions (50).

6. The method according to any one of the preceding claims, wherein the additional spatial encoding field comprises spatially-temporally arbitrary magnetic fields, including linear and / or nonlinear fields in arbitrary time-domain modulations.

7. The method according to any one of the preceding claims, wherein the spatial encoding field is driven by a periodic time-domain modulation signal, for example, a sinusoidal modulation signal, wherein the modulation period of the periodic modulation signal is set as a multiple integer of the MRI scanner dwell time for synchronization in timing.

8. The method according to any one of the preceding claims, wherein a resolution of the first MRI data (10) is lower than a resolution of a final object image reconstructed by using the calibrating of the additional spatial encoding field, and / or the second MRI data is undersampled with less acquisition time compared to a fully sampled k-space data without the additional spatial encoding field.

9. The method according to any one of the preceding claims, wherein a k-space neighbourhood (20) of the first MRI data (10) or second MRI data (15) represents a selected subset of acquired data points in the Fourier domain of the object image, centred around the k-space location at the acquisition time (ts).

10. The method according to any one of the preceding claims, wherein no other field mapping scans additional to the first and second MRI data collection scans are performed for determining the spin phase evolution maps (60) caused by the additional spatial encoding field (A'B).

11. Method of magnetic resonance imaging, MRI, an object, comprising the steps of: providing an MRI scanner (100); acquiring first MRI data (10) by a first MRI data collection scan, wherein an object (1) is subjected to a static magnetic field (B0), magnetic field gradients (ABO), and RF coil fields (B , generated by the MRI scanner (100);acquiring second MRI data (15) by a second MRI data collection scan, wherein the object (1) is subjected to the static magnetic field (BO), the magnetic field gradients (ABO), the RF coil fields (Bl) generated by the MRI scanner and an additional superimposed spatial encoding field (A'B), generated by the MRI scanner (100) or an additional field generating hardware component; and calibrating (S300) the MRI data according to a method of any one of the preceding claims.

12. Method according to claim 11, wherein the MRI scanner (100) comprises at least one local magnetic field coil (115) being arranged adjacent to the object (1) for generating the additional spatial encoding field (A'B).

13. Computer program product comprising a sequence of machine instructions which causes a computer performing a method according to any one of the preceding claims, when executing the sequence of machine instructions.

14. Medium on which a computer program product according to claim 13 is stored.

15. Computer on which a computer program product according to claim 13 is stored and which is processable by the computer.

16. Computer according to claim 15, characterized in that, it is formed as a control device for an MRI scanner.

17. Magnetic Resonance Imaging, MRI, scanner comprising a control device which is configured to perform a method according to any of claims 1-12 or a computer according to claim 15 or 16.

Images