Method for estimating object motion and / or magnetic field offset during an MRI scan - Patents.com

Abstract

In a method for estimating an object's motion and / or a magnetic field offset in a region surrounding the object during a magnetic resonance (MR) imaging scan of the object, superimposed magnetic and radio frequency magnetic fields are generated according to an MR sequence for forming an image, the MR sequence including a series of sequence modules, each sequence module including a radio frequency (RF) excitation segment and an image encoding gradient segment, the MR sequence further including a plurality of navigator gradient segments. The navigator signals are collected along a trajectory in k-space and are represented as a discrete time series including a predefined number of complex-valued signal data points. The navigator signals collected in a first sequence module are used to calculate a transformation matrix that relates the rotation angle and translation amount and / or the magnetic field changes to the corresponding changes in the navigator signals in a first approximation. The navigator signals collected in subsequent sequence modules are used to estimate the object's motion in terms of the object's translational and rotational displacements by solving corresponding linear least squares estimation problems, and / or to estimate the magnetic field offset in terms of the scalar and vector magnetic field changes between the first sequence module and the subsequent sequence module.

Description

[Technical field]

[0001] The present invention relates generally to a method for estimating object motion and / or magnetic field offset during a magnetic resonance (MR) imaging scan of the object. [Background technology]

[0002] Patient motion is one of the major causes of image artifacts in MR imaging. Many different methods for motion correction have been developed during the past decades (Non-Patent Documents 1-3). The k-space navigator is a particularly promising method since it is a purely MR signal-based method that does not require any additional hardware.

[0003] Navigator-based motion estimation methods are described, inter alia, in US Pat. No. 6,399,433 and US Pat. No. 6,499,446. [Prior art documents] [Patent documents]

[0004] [Patent Document 1] U.S. Patent No. 6,771,068 [Patent Document 2] U.S. Patent No. 7,358,732 [Non-patent literature]

[0005] [Non-Patent Document 1] Zaitsev Maxim, Maclaren Julian and Herbst Michael, "Motion artifacts in MRI: A complex problem with many partial solutions", Journal of Magnetic Resonance Imaging, Vol. 42, pp. 887-901, 2015. [Non-Patent Document 2] Godenschweger, F. et al., "Motion correction in MRI of the brain," Phys. Med. Biol., Vol. 61, p. R32, 2016. [Non-Patent Document 3] Maclaren, J., Herbst, M., Speck, O., and Zaitsev, M., "Prospective motion correction in brain imaging: A review," Magnetic Resonance in Medicine, Vol. 69, pp. 621-636, 2013. Summary of the Invention [Problem to be solved by the invention]

[0006] A primary objective of the present invention is to overcome the limitations and drawbacks of currently known methods. [Means for solving the problem]

[0007] According to one aspect of the invention, there is provided a method for estimating motion of an object during a magnetic resonance (MR) imaging scan of the object, comprising: generating a main magnetic field in the object of interest by a main magnet; and generating superimposed magnetic and radio frequency magnetic fields in accordance with an MR sequence to form an image; - an MR sequence includes a sequence of sequence modules; - each sequence module includes a radio frequency (RF) excitation segment and an image encoding gradient segment; - the MR sequence further comprises a plurality of navigator gradient segments; in this way, - during a measurement segment of each sequence module, object signals are acquired using an RF receiving coil or coil array; During each of the navigator gradient segments, navigator signals are acquired using the RF receive coil.

[0008] The term "subject" shall be understood to include any object suitable for magnetic resonance imaging. In particular, the term shall include any human or animal subject, including a human patient in need of diagnostic and / or therapeutic intervention.

[0009] According to this aspect, - said navigator signals are acquired along a trajectory k(t) in k-space; The navigator signal in a given sequence module is represented as a discrete time series containing a predefined number N of complex-valued signal data points. s(k(t i )), where i=1~N, - the navigator signal s(k(t i ) is used to calculate a transformation matrix M that relates, to a first approximation, the rotation angles and translational movements to corresponding changes in the navigator signals; - Navigator signals collected in the subsequent sequence module

[0010]

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[0011] Using the linear least squares estimation problem

[0012]

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[0013] By solving: the motion of the object is estimated in terms of its translational displacement Δx and rotational displacement θ between the first sequence module and the subsequent sequence module. For the sake of brevity, the navigator signals collected in the subsequent sequence modules

[0014]

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[0015] "Subsequent navigator signals

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[0017] Furthermore, for clarity and easier notation, the method will first be described without reference to a multi-channel RF receive array. Thereafter, a method for processing navigator signals collected using a multi-channel array will be described.

[0018] Advantageous embodiments are defined below and in the dependent claims. The present invention relies on the principle that rotation of the imaged object causes a corresponding rotation of the k-space signal, and translation causes a linear phase shift in the signal. These are known properties of the Fourier transform. Formally, s(k(t)) and

[0019]

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[0020] denoting the k-space signal before and after application of a 3×3 rotation matrix R(θ) and a three-dimensional (3D) translation of vector Δx, we obtain:

[0021]

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[0022] where θ = (θ1, θ2, θ3). T denotes a column vector of three rotation angles, each around one of the coordinate axes. Similarly, Δx=(Δx1,Δx2,Δx3) Tis a three-element column vector that represents the translational displacements along the three coordinate axes. If the rotation angle and translation vector are small, the above equation can be approximated by a first order Taylor expansion, which can be written as a linear function of the angle and the amount of movement.

[0023]

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[0024] needs to be interpreted as a function of the rotation angle θ and the amount of movement Δx. The assumption of small rotation angles and movements is satisfied when the imaged object only undergoes small movements during the imaging scan. If the object undergoes larger movements, this assumption is usually still satisfied if the estimated motion parameters are immediately fed back to the MR scanner system, and the scanner corrects the object motion in real time, as described in US Pat. No. 6,771,068 B2. In particular, the orientation of the scanner gradient coordinate system must follow the rotation of the imaged object. Furthermore, a phase offset must be added to the navigator and imaging signals to compensate for the translation of the object.

[0025] It is straightforward to calculate the derivatives of the above equation with respect to Δx1, Δx2, and Δx3 because the complex exponential function has the known power series expansion:

[0026]

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[0027] Determining the derivatives (or approximations) of the equation with respect to the rotation angles θ1, θ2, and θ3 is more difficult, and will be explained later. These derivatives are denoted as ds / dθ d θ d If we denote it by (d=1,2,3), the Taylor expansion becomes:

[0028]

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[0029] Theoretically, the derivative ds / dθ d can be calculated using the chain rule of differentiation: ds / dθ d =∂s / ∂k ∂ / ∂θ d [R(θ)k(t)] However, in practice, the partial derivative ∂s / ∂k is unknown. Instead, if we interpret the signal s(k(t)) as a function of time, we obtain the time derivative

[0030]

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[0031] can be calculated. This is

[0032]

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[0033] is the directional derivative of s(k(t)) in the direction of t, and is the tangent vector of the navigator's k-space trajectory:

[0034]

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[0035] From linear algebra, it is known that given two vectors v and w, the vector v can be written as a sum of two vectors, the first of which is parallel to w and the second of which is orthogonal to w. The first of these two vectors is also called the orthogonal projection of v onto w. Thus, the rotational displacement ∂ / ∂θ d [R(θ)k(t)] is the tangent component of the k-space trajectory (

[0036]

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[0037] (multiples of ) and

[0038]

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[0039] and a component orthogonal to

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[0041] Combining the last three equations, we get the derivative ds / dθ d It can be seen that it can be divided into tangential and orthogonal parts.

[0042]

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[0044] To compute the derivative in any direction orthogonal to , k-space data from the neighborhood of the navigator trajectory is required, which is unsampled. One practical solution to this problem, here denoted as η d The derivative ds / dθ is d The key is to consider only the tangential component of

[0045]

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[0046] Alternatively, the full derivative ds / dθ can be calculated by a finite difference reference measurement under small rotations. dFor a sufficiently small angle α, the derivative can be found as follows:

[0047] ds / dθ d ≒1 / α[s(R(α e d )k(t))-s(k(t))] Here, e d denotes the d-th fundamental unit vector. The navigator signal s(R(α e d )k(t)) are collected for small rotations about each of the three coordinate axes. In other words, the transformation matrix M is a set of initial navigator signals, i.e., the set of subsequent navigator signals, all of which are used to estimate the object motion.

[0048]

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[0049] The navigator signal s(k(t i )) and navigator signals s acquired by one or more sequence modules. j (k(t i )) is calculated.

[0050] Since the measurement noise of the complex-valued navigator signal follows a zero-mean Gaussian distribution, we calculate the angle θ and the translation vector Δx by linear least-squares estimation. The spectrometer is n We sample the MR signal only at t k = t t . It is advantageous to write the estimation problem in matrix-vector form. We define the following matrix M that relates rotation angles and translations to signal perturbations. Each row of M represents the signal value s(k(t i )) at one time point t i The first three columns of M represent the derivatives of the signal with respect to the displacements Δx1, Δx2, and Δx3. The last three columns represent the derivatives (or approximations thereof) with respect to the rotation angles θ1, θ2, and θ3.

[0051]

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[0052] The sampled MR signals are denoted by a column vector s.

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[0054] If we are stuck at , we need to solve the following linear least-squares estimation problem:

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[0056] According to an advantageous embodiment (claim 2), this is done by multiplication of the signal vector with the Moore-Penrose pseudoinverse of M.

[0057]

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[0058] Considering typical acquisition bandwidths in magnetic resonance imaging and expected readout times of the navigator signals, the number of rows of the matrix M is significantly larger than the number of columns. Therefore, the estimation problem is highly overdetermined.

[0059] It will be clear to those skilled in the art that apart from the application of the Moore-Penrose pseudoinverse, there are many different established methods for computing the solution to the least-squares estimation problem above. These include, among others, QR decomposition or singular value decomposition (SVD). Furthermore, instead of computing the exact solution, the solution can be approximated using methods such as the Conjugate Gradient (CG) algorithm. To improve the conditioning of the estimation problem, some form of regularization may be applied to the matrix M. The most common choice is the Tikhonov regularization, but many other variations are possible.

[0060] If the navigator signals are collected using an RF coil array with several separate receive channels, the matrix M can be calculated separately for the navigator signals from each receive channel. c ,

[0061]

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[0062] denotes the signal collected from channel c, and M c If x denotes the matrix computed from only the signal from channel c, then θ and Δx can be computed by introducing a summation over the receive channels in the linear least-squares problem as follows:

[0063]

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[0064] Alternatively, the signal values ​​from the separate receive channels can be combined into one virtual receive channel using a weighted sum. This process is known in the MRI literature as coil compression or array compression. The matrix M, and ultimately the values ​​of θ and Δx, are calculated from the combined navigator signals.

[0065] Briefly, the present invention relies on a new algorithm for navigator-based motion estimation that uses a linear perturbation model of complex-valued signal variations to estimate rotation and translation with high accuracy and low computational complexity.

[0066] The timing of the navigator gradient segments can be selected according to other requirements of the MRI scan. It will be appreciated that the temporal separation between subsequent navigator gradient segments should be small enough to allow for the neglect of higher order terms in the applied formalism.

[0067] According to an advantageous embodiment (claim 3), one navigator gradient segment is executed in each of the sequence modules. In other embodiments, a navigator gradient segment is applied, for example, to every other or every third sequence module. In principle, a series of non-equidistant navigator gradient segments can also be applied.

[0068] It is also understood that the navigator gradient segments should be applied to appropriate regions of the MR sequence, i.e. regions that do not overlap with an RF excitation segment or an image encoding segment. According to an advantageous embodiment (claim 4), each navigator gradient segment of a respective sequence module is executed between the RF excitation segment and the image encoding segment of said respective sequence module. According to another advantageous embodiment (claim 5), each navigator gradient segment of a respective sequence module is executed after the image encoding segment of said respective sequence module but before the RF excitation segment of the sequence module following said respective sequence module.

[0069] According to a further aspect of the invention (claim 6), there is provided a method for estimating a magnetic field offset in a region surrounding an object during a magnetic resonance (MR) imaging scan of the object. Using the same principles as the Taylor expansion and linear least squares estimation, the magnetic field offset can also be estimated. The MR signal of an object placed in the bore of the scanner, whose transverse magnetization is described by a function ρ(x) of the three-dimensional spatial coordinate x, is given by:

[0070]

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[0071] For an unwanted offset in the magnetic field, ΔB(x,t), the formula changes to:

[0072]

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[0073] To estimate the magnetic field offset ΔB(x,t), it must first be parameterized so that it can be expressed by a finite number of parameters. Therefore, a set of basis functions is selected that is considered suitable for expressing the magnetic field offset. One natural choice of parameterization for the spatial coordinate x is a subset of spherical harmonics (e.g., up to second or third order) in a wide range of common magnetic field expansions. For the time coordinate t, for example, a polynomial basis can be selected.

[0074] The zeroth order spherical harmonic describes a spatially uniform magnetic field offset. In particular, if the offset is constant with respect to position x and acquisition time t (during a single navigator acquisition), then:

[0075]

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[0076] The effect of such a background field offset during encoding is equivalent to multiplying the unperturbed signal by a phase offset that is linear in time.

[0077]

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[0078] First order spherical harmonics describe magnetic fields that increase linearly in one of the three coordinate directions (so-called gradient fields). Gradient fields are linear in position x and therefore take the form ΔB(x,t)=G1x1+G2x2+G3x3 (assuming they are constant in time), where the coefficients G d are scalars indicating the gradient strengths in the three coordinate directions.

[0079]

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[0080] The effect of these background field gradients is shown in the modified k-space trajectory

[0081]

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[0082] This is equivalent to collecting the signal at

[0083]

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[0084] As in the case of rotation estimation, the displacement coefficient λ d (t) can be calculated.

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[0086] For rotational and translational estimation, we construct a matrix Q that relates the magnetic field offset parameters to the resulting signal changes.

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[0088] This matrix is ​​used to calculate the magnetic field parameters by linear least squares estimation.

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[0090] Besides the spatially uniform (ΔB0) and spatially linear (G1, G2, G3) magnetic field offsets, the same principle can be used equally well with any other set of basis functions that are considered suitable for developing the expected magnetic field offsets. One natural choice is a subset of spherical harmonics (e.g., up to second or third order) among a wide range of common magnetic field expansions. The magnetic field expansion may also be specially selected for a given object, subject or body part, using prior measurements (e.g., by magnetic field mapping) or simulations to determine suitable basis functions. In each of these cases, to develop the proposed method, the key step is to determine the derivatives of the navigator signals with respect to the coefficients of the magnetic field expansion, which form the columns of the model matrix Q. Depending on the basis functions, these derivatives or their approximations may be analytically available or must be determined by measurement or simulation. For the measurement of the signal derivatives, one option is to first collect the navigator signals in a reference state, and then collect the navigator signals again in the presence of small magnetic field offsets of the spatial structure given by the basis functions in question. A good approximation of the derivative is given by the difference of the navigator signal divided by the strength of the perturbation of the scale of the basis function. This option is simple, for example, in the case of a basis formed from magnetic field patterns that can be generated with available gradient and shim coils. The available gradient and shim magnetic fields form a particularly advantageous basis in that they not only easily allow the measurement of the respective signal derivatives, but also allow active compensation of the magnetic field offset once detected by the operation of the same gradient and shim channels.

[0091] Furthermore, besides any spatial pattern, the basis functions for the magnetic field evolution can also be given a temporal variation over the duration of the navigator acquisition. One natural choice is to use the powers of time (1,t,t), which allows the determination of a Taylor series with respect to time. 2 ,t 3…) Another useful option is the exponential decay over time (e -at ) With any combination of spatial and temporal variations selected for each basis function, the corresponding columns of the Q matrix are given by the derivatives of the navigator signals with respect to the associated expansion coefficients, determined analytically, by measurement, or by simulation.

[0092] According to a further aspect of the invention (claim 7), there is provided a method for estimating (i) the motion of an object and (ii) the magnetic field offset in a region surrounding the object during a Magnetic Resonance (MR) imaging scan of the object, which combines the above mentioned aspects and relies on a transformation matrix R combining the matrices M and Q defined above, i.e. a matrix having the following rows:

[0093]

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[0094] Further aspects of the invention are defined in claims 7, 8 and 9, which are explained hereinafter. The estimated rotation angles, translations and / or magnetic field offsets can be used to compensate for the effects of object motion and magnetic field offsets in real time during the scanning procedure, which is commonly referred to as prospective correction.

[0095] Briefly, object motion is compensated for in real time by realigning the imaging volume to the rotated and moved object. Object rotation is compensated for by rotating the subsequent gradient waveforms accordingly. Translation is corrected by adding a linear phase offset to the subsequent MR signals.

[0096] Since a constant magnetic field offset adds a phase to the MR signal that is linear with acquisition time, the magnetic field offset can be compensated for by removing this phase offset from the signal values. Higher order magnetic field offsets can be compensated for using shim coils in the MR system.

[0097] Alternatively, the effects of object motion and / or magnetic field offsets can be compensated for during image reconstruction after the scan is completed, which is commonly referred to as retrospective correction.

[0098] Prospective and retrospective corrections can also be combined. This is useful, for example, when the real-time corrections cause a time delay between estimating the motion and magnetic field parameters and applying the compensation. In this case, the retrospective correction can be used to correct residual errors that could not be compensated during the prospective corrections due to the time delay.

[0099] For all the above-mentioned embodiments of estimation (of motion parameters, magnetic field offset parameters, or both), it is advantageous to use the resulting estimates for active compensation during each MRI scan. Active compensation of motion is typically performed by corresponding rotation and translation of the coordinate system in which the MRI sequence including the navigator is deployed. This concept is known as prospective motion correction (PMC). Active compensation of magnetic field offset is performed by corresponding gradient and shim application and zero-order shim (homogeneous magnetic field) application, or equivalently signal demodulation. Importantly, in addition to removing errors from the acquired image data, such compensation mimics the reference situation in which the reference navigator was acquired, so that the increment of motion and magnetic field offset detected at each individual iteration of the navigator is small and therefore consistent with the first-order perturbation method that is the basis of this methodology.

[0100] Perturbations of the collected raw image data, with or without runtime compensation, due to residual effective motion and / or magnetic field offsets can be addressed at the image reconstruction stage, which is typically numerically best (optimally tuned) when the underlying effective motion and magnetic field offsets are small. Correcting detected motion and magnetic field offsets at the reconstruction level is therefore generally most effective in combination with preceding runtime compensation.

[0101] The above-mentioned and other features and objects of the present invention, as well as the manner in which they are accomplished, will become more apparent, and the invention itself will be better understood, by referring to the following description of various embodiments of the present invention in conjunction with the accompanying drawings, in which: [Brief description of the drawings]

[0102] [Figure 1] FIG. 13 shows a sequence diagram of a 3D T2*-weighted FFE sequence in which a 3D trajectory navigator gradient is inserted after excitation and before the image encoding gradient. [Figure 2a] 13 is a trajectory navigator k-space trajectory and a parametric plot of the trajectory shape. [Figure 2b] FIG. 1 shows a trajectory navigator k-space trajectory with plots of trajectory, gradient and slew rate over time; the trajectory is composed of three orthogonal circles with smooth transitions between them; at a radius of 200 rad / m, the navigator gradient can be executed in approximately 1.65 milliseconds. [Figure 3a] The rotation angle (top) and translation amount (bottom) estimated from an experiment using a stationary phantom (pineapple) are shown. [Figure 3b] The standard deviation (bottom) and root mean square (top) of rotational angle and translational parameters over time are shown. [Figure 4a] Motion parameters estimated from an in vivo experiment in which volunteers were instructed to remain stationary: rotation about the AP axis (top panel) and translation along the anterior-posterior (AP) axis (bottom panel). [Figure 4b]Spectra of movement time series for two selected axes are shown: the spectrum of rotation around the left-right (LR) axis, which shows a spectral peak at 1.22 Hz (top panel), and the spectrum of movement along the head-foot (HF) axis, which shows a peak at 0.30 Hz (bottom panel). [Diagram 5] We show the estimated motion parameters in terms of rotation angle (top panel) and estimated motion parameters related to the amount of movement (bottom panel) from an in vivo experiment where volunteers were instructed to move their head randomly in all six degrees of freedom. [Figure 6] 1 shows a schematic diagram of one embodiment of a method for estimating motion using a combination of prospective and retrospective corrections; [Figure 7] 4 shows a schematic diagram of a second variant of the method for estimating motion by combining prospective and retrospective corrections; DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0103] As is commonly known in the MR field, an MR sequence includes a train of sequence modules with a sequence repetition period TR between each set of successive sequence modules. One such sequence module is shown diagrammatically in Figure 1, which also shows a set of navigator gradient segments, which in the illustrated example are located after excitation and before the image encoding gradient segments.

[0104] (Example) Experiments were performed on a 7T Philips Achieva scanner using a 32-channel head coil. A single-shot 3D orbital navigator (Ulrich, T., Patzig, F., Wilm, BJ, and Pruessmann, KP, "Towards Optimal Design of Orbital K-Space Navigators for 3D Rigid-Body Motion Estimation", ISMRM & SMRT Virtual Conference & Exhibition, 2020) shown in Figure 2 was used.

[0105] To examine the accuracy of the method, a stationary phantom (pineapple) was placed inside the head coil. * Navigator signals were acquired during the w-FFE imaging scan, and motion parameters were estimated from the navigator signals.

[0106] Two in vivo experiments were also performed. In the first experiment, volunteers were instructed to remain stationary during a 2.5 minute FFE scan sequence. During the second experiment, volunteers were instructed to move their head in all six degrees of freedom. The motion parameters were estimated using the algorithm proposed in this application.

[0107] The results of the experiment with the static phantom are shown in Figure 3. The algorithm yielded rotation angles in the range of ±0.15 degrees and translations in the range of ±60 μm, with root-mean-square values ​​of up to 0.04 degrees and 25 μm.

[0108] Figures 4 and 5 show the estimated rotation angle and translation from two in vivo experiments. During the experiment without intentional movement, the rotation was estimated to be within ±0.2 degrees and ±0.25 mm, but for the HF axis, the estimated translation value appears to drift and oscillate around -0.2 mm. The spectrum showed clear peaks at 0.30 Hz and 1.22 Hz.

[0109] When volunteers moved purposefully, the algorithm of the present application reported rotation angles of up to ±2 degrees and movements of ±3.5 mm. Phantom experiments demonstrate the high precision and accuracy of the method of the present application. Knowing that no real object motion occurs, it can be concluded that the estimates of the method of the present invention are accurate to a maximum of 0.04 degrees, with an RMS error of 25 μm, and the standard deviation is approximately the same magnitude.

[0110] Unfortunately, ground truth is not available for in vivo experiments. However, the results show that our algorithm is highly sensitive to head motion. The spectral peaks at 0.30 Hz and 1.22 Hz are likely due to breathing and heartbeat. The accuracy and precision of head motion estimation will be further investigated in the future.

[0111] In conclusion, we have demonstrated that our motion estimation algorithm can be used to characterize rigid body motion accurately and with high precision. Because the navigator readout is very fast and the algorithm has very low computational complexity, the motion parameters can be calculated within milliseconds.

[0112] A first variation of the method for estimating motion by combining prospective and retrospective correction is shown in FIG. A second variant of the combined prospective and retrospective correction method for estimating motion is shown in FIG.

Claims

1. 1. A method of estimating motion of an object during a magnetic resonance (MR) imaging scan of the object, comprising: generating a main magnetic field in the object by a main magnet; and generating superimposed magnetic and radio frequency magnetic fields in accordance with an MR sequence to form an image; said MR sequence comprises a sequence of sequence modules, each sequence module includes a radio frequency (RF) excitation segment and an image encoding gradient segment; said MR sequence further comprises a plurality of navigator gradient segments; In the method During the measurement segment of each sequence module, object signals are acquired using an RF receiving coil or coil array, During each of the navigator gradient segments, navigator signals are acquired using the RF receive coil or coil array. In the method, said navigator signals are acquired along a trajectory k(t) in k-space, The navigator signal in a given sequence module is represented as a discrete time series containing a predefined number N of complex-valued signal data points. s(k(t ｉ )), where i = 1~N, A transformation matrix M that relates, in a first approximation, the rotation angles and translational displacements to the corresponding changes in the navigator signals s(k(t ｉ )) is calculated from - Navigator signals acquired in the subsequent sequence module [0010] Using the linear least squares estimation problem [0025] The motion of the object is estimated in terms of the translational displacement Δx and the rotational displacement θ of the object between the first sequence module and the subsequent sequence module by solving A method comprising:

2. The linear least squares estimation problem is solved by solving the Moore-Penrose pseudoinverse matrix M ＋ 2. The method of claim 1, wherein the motion estimation is solved by multiplication with

3. The method of claim 1 or 2, wherein one navigator gradient segment is executed in each of the sequence modules.

4. 4. The motion estimation method of claim 3, wherein the navigator gradient segment of each sequence module is performed between the RF excitation segment and the image encoding gradient segment of the each sequence module.

5. 4. The motion estimation method of claim 3, wherein each navigator gradient segment of a respective sequence module is performed after the image encoding gradient segment of the respective sequence module but before the RF excitation segment of the sequence module following the respective sequence module.

6. 1. A method of estimating a magnetic field offset in a region surrounding an object during a magnetic resonance (MR) imaging scan of the object, comprising: generating a main magnetic field in the object by a main magnet; and generating superimposed magnetic and radio frequency magnetic fields in accordance with an MR sequence to form an image; said MR sequence comprises a sequence of sequence modules, each sequence module includes a radio frequency (RF) excitation segment and an image encoding gradient segment; said MR sequence further comprises a plurality of navigator gradient segments; In the method During the measurement segment of each sequence module, object signals are acquired using an RF receiving coil or coil array, During each of the navigator gradient segments, navigator signals are acquired using the RF receive coil or coil array. In the method, said navigator signals are acquired along a trajectory k(t) in k-space, The navigator signal in a given sequence module is represented as a discrete time series containing a predefined number N of complex-valued signal data points. s(k(t ｉ )), where i = 1~N, a transformation matrix Q relating in a first approximation the changes in the main magnetic field to corresponding changes in the navigator signals s(k(t ｉ )) is calculated from - Navigator signals acquired in the subsequent sequence module [0030] Using the linear least squares estimation problem [0045] By solving the zero-order magnetic field variation ΔB between the first sequence module and the subsequent sequence module, ０ and the primary magnetic field fluctuation [0050] The magnetic field offset is estimated for A method comprising:

7. 1. A method of estimating motion and magnetic field offsets of an object in a region surrounding the object during a magnetic resonance (MR) imaging scan of the object, comprising: generating superimposed magnetic and radio frequency magnetic fields in accordance with an MR sequence to form an image; said MR sequence comprises a sequence of sequence modules, each sequence module includes a radio frequency (RF) excitation segment and an image encoding gradient segment; said MR sequence further comprises a plurality of navigator gradient segments; In the method During the measurement segment of each sequence module, object signals are acquired using an RF receiving coil or coil array, During each of the navigator gradient segments, navigator signals are acquired using the RF receive coil or coil array. In the method, said navigator signals are acquired along a trajectory k(t) in k-space, The navigator signal in a given sequence module is represented as a discrete time series containing a predefined number N of complex-valued signal data points. s(k(t ｉ )), where i = 1~N, A transformation matrix R that relates, in a first approximation, the rotation angle, the translation amount, and the changes in the main magnetic field to the corresponding changes in the navigator signals s(k(t ｉ )) is calculated from - Navigator signals acquired in the subsequent sequence module [006] Using the linear least squares estimation problem [0070] The motion of the object is estimated in terms of the translational displacement Δx and rotational displacement θ of the object by solving ０ and vector magnetic field fluctuations [0080] The magnetic field offset is estimated for A method comprising:

8. A method for prospectively correcting motion of an object and / or magnetic field offset in a region surrounding the object during a magnetic resonance (MR) imaging scan of the object, comprising: performing a method as described in any one of claims 1, 2, 6, and 7 to provide an estimate of the object's motion and / or the magnetic field offset, and using the estimate to correct subsequent executions of the sequence module including the navigator signal.

9. 8. A method for retrospectively correcting motion of an object and / or magnetic field offset in a region surrounding the object during a magnetic resonance (MR) imaging scan of the object, comprising: performing a method as claimed in any one of claims 1, 2, 6 and 7 to provide an estimate of the object's motion and / or the magnetic field offset, and using the estimate to correct MR images reconstructed from the MR sequence.

10. 10. A method for correcting a motion of an object and / or a magnetic field offset in a region surrounding the object during a magnetic resonance (MR) imaging scan of the object, comprising: performing a method according to any one of claims 1, 2, 6 and 7 to provide an estimate of the motion of the object and / or the magnetic field offset, the estimate being used to correct a subsequent execution of the sequence module including the navigator signal; A method in which an estimate of the object motion and / or the magnetic field offset is provided, and said estimate is used to correct MR images reconstructed from the MR sequence.

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