EPI GHOST CORRECTION INVOLVING SENSE

Abstract

In an EPI acquisition sequence for magnetic resonance signals k-space is scanned along sets of lines in k-space along opposite propagation directions, e.g. odd and even lines in k-space. Phase errors that occur due to the opposite propagation directions are corrected for in a SENSE-type parallel imaging reconstruction. The phase error distribution in image space may be initially estimated, calculated form the phase difference between images reconstructed from magnetic resonance signals acquired from the respective sets of k-space lines, or from an earlier dynamic.

Claims

1. A magnetic resonance imaging method which comprises an echo-planar imaging (EPI) acquisition sequence which includes sampling of k-space for magnetic resonance signals to collect a ltr-data set (m.sub.ltr) reconstructed from lines in k-space scanned along a positive traversal direction in k-space and a rtl-data set (m.sub.rtl) reconstructed from lines in k-space scanned along a negative traversal direction in k-space, the magnetic resonance signals of the ltr-data set and the rtl-data set being acquired with several RF receiver antennae having spatial sensitivity profiles accessing a spatial phase error distribution for the ltr-data set and for the rtl-data set forming a ltr-encoding matrix (S.sub.ltr) from (i) the phase encoding of the lines in k-space scanned along a positive traversal direction in k-space, (ii) the spatial phase error distribution for the ltr-data set, and (iii) the spatial coil sensitivity profiles, forming a rtl-encoding matrix from (S.sub.rtl) (i) the phase encoding of the lines in k-space scanned along a negative traversal direction in k-space, (ii) the spatial phase error distribution for the rtl-data set, and (iii) the spatial coil sensitivity profiles, combining the ltr-encoding matrix and the rtl-encoding matrix into a global encoding matrix S, reconstructing a diagnostic magnetic resonance image (p) by resolving the encoding relationship between the ltr and rtl-data sets for the pixel-values (p.sub.j(r)) of the magnetic resonance image: $\mathrm{Sp}=\left[\begin{array}{c}{S}_{\mathrm{ltr}}\\ S_{\mathrm{rtl}}\end{array}\right].Math.p=\left(\begin{array}{c}{m}_{\mathrm{ltr}}\\ m_{\mathrm{rtl}}\end{array}\right)$ and, wherein the ltr-data set and/or rtl-data set is/are undersampled in k-space and an unfolded ltr-image is derived from the ltr-data set as a solution of the encoding relationship between the ltr-data set and the pixel values of the unfolded ltr-image: S.sub.ltrp.sub.ltr=m.sub.ltr, an unfolded rtl-image is derived from the rtl-data set as a solution of the encoding relationship between the rtl-data set and the pixel values of the unfolded rtl-image: S.sub.rtlp.sub.rtl=m.sub.rtl and a subtraction phase image is formed from the unfolded ltr-image and the unfolded rtl-image, and employ the subtraction phase image as the spatial phase error distribution and wherein an initial spatial phase error distribution is measured in a calibration stage, a phase corrected unfolded ltr-image is formed in that the unfolded ltr-image or the ltr-data set is corrected by the initial spatial phase error distribution a phase corrected unfolded rtl-image is formed in that the unfolded ltr-image or the rtl-data set is corrected by the initial spatial phase error distribution and the subtraction phase image is formed from the phase corrected unfolded ltr-image and the phase corrected unfolded rtl-image and in which the phase corrected ltr-image and the phase corrected rtl-image are generated in an iterative manner.

2. The magnetic resonance imaging method as claimed in claim 1, in which the resulting phase corrected unfolded ltr-image and phase corrected unfolded rtl-image are employed to derive a more accurate subtracted phase image which provides a spatial phase error distribution of the current iteration, which, in particular, in turn is employed in a next iteration to again correct for phase errors in the unfolded ltr-image and unfolded rtl-image.

3. The magnetic resonance imaging method as claimed in claim 1 wherein the initial spatial phase error distribution is measured in the calibration stage in which an EPI acquisition is done having one set of lines in k-space each scanned first along a positive and then along a negative propagation direction and having another set of lines in k-space each scanned first along a negative and then along a positive propagation direction.

4. The magnetic resonance imaging method of claim 3 in which a line along zero-phase encoding is scanned in k-space first along a positive traversal, then along a negative traversal and finally again along a positive traversal.

5. A computer program for controlling a magnetic resonance examination system and comprising instructions stored on a non-transitory computer readable medium, which when executed casuses the magnetic resonance examination system to apply an echo-planar imaging (EPI) acquisition sequence which includes sampling of k-space for magnetic resonance signals to collect a ltr-data set (m.sub.ltr) reconstructed from lines in k-space scanned along a positive traversal direction in k-space and a rtl-data set (m.sub.rtl) reconstructed from lines in k-space scanned along a negative traversal direction in k-space, acquire the magnetic resonance signals of the ltr-data set and the rtl-data set with several RF receiver antennae having spatial sensitivity profiles accessing spatial phase error distributions for the ltr-data set and for the rtl-data set forming a ltr-encoding matrix (S.sub.ltr) from (i) the phase encoding of the lines in k-space scanned along a positive traversal direction in k-space, (ii) the spatial phase error distribution for the ltr-data set, and (iii) the spatial coil sensitivity profiles, forming a rtl-encoding matrix from (S.sub.rtl) (i) the phase encoding of the lines in k-space scanned along a negative traversal direction in k-space, (ii) the spatial phase error distribution for the rtl-data set, and (iii) the spatial coil sensitivity profiles, combining the ltr-encoding matrix and the rtl-encoding matrix into a global encoding matrix S, reconstructing a magnetic resonance image (p) by resolving the encoding relationship between the ltr and rtl-data sets and the pixel-values (p.sub.j(r)) of the magnetic resonance image: $\left[\begin{array}{c}{S}_{\mathrm{ltr}}\\ S_{\mathrm{rtl}}\end{array}\right].Math.p=\left(\begin{array}{c}{m}_{\mathrm{ltr}}\\ m_{\mathrm{rtl}}\end{array}\right)$ and to undersample the ltr-data set and/or rtl-data set in k-space and to derive an unfolded ltr-image from the ltr-data set as a solution of the encoding relationship between the ltr-data set and the pixel values of the unfolded ltr-image: S.sub.ltrp.sub.ltr=m.sub.ltr to derive an unfolded rtl-image is derived from the rtl-data set as a solution of the encoding relationship between the rtl-data set and the pixel values of the unfolded rtl-image: S.sub.rtlp.sub.rtl=m.sub.rtl and to from a subtraction phase image from the unfolded ltr-image and the unfolded rtl-image, and employ the subtraction phase image as the spatial phase error distribution and to measure an initial spatial phase error distribution in a calibration stage, to form a phase corrected unfolded ltr-image in that the unfolded ltr-image or the ltr-data set is corrected by the initial spatial phase error distribution to from a phase corrected unfolded rtl-image in that the unfolded ltr-image or the rtl-data set is corrected by the initial spatial phase error distribution and to form the subtraction phase image from the phase corrected unfolded ltr-image and the phase corrected unfolded rtl-image and in which the phase corrected ltr-image and the phase corrected rtl-image are generated in an iterative manner.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0025] FIG. 1 shows a schematic representation of an implementation of the magnetic resonance imaging method of invention;

[0026] FIG. 2 shows a representation of an example of a two-dimensional k-space EPI trajectory for the calibration stage to measure the initial spatial phase error distribution is measured;

[0027] FIG. 3 shows a diagrammatic representation of a magnetic resonance examination system in which the present invention is incorporated.

DETAILED DESCRIPTION OF THE EMBODIMENTS

[0028] FIG. 1 shows a diagrammatic representation of an implementation of the magnetic resonance imaging method of invention. In the single-shot EPI acquisition 101 two-dimensional k-space is scanned along lines in the positive propagation direction (left-to-right) and in the negative propagation direction (right-to-left). The data acquired in this manner form the ltr-data set and the rtl-data set. Typically, odd lines and even lines are scanned along opposite directions. From the data acquired by scanning along the positive propagation directions (e.g. the odd lines), that is from the ltr-data set the folded ltr-image 102 is reconstructed, typically by a fast-Fourier transformation of the ltr-data set. From the data acquired by scanning along the positive propagation directions (e.g. the odd lines), that is from the rtl-data set the folded rtl-image 103 is reconstructed, typically by a fast-Fourier transformation of the ltr-data set. Usually, the ltr-data (rtl-data) set formed by only the odd (even) lines will be under sampled in the phase-encoding direction in k-space giving rise to aliasing that manifests itself as folding artefacts. The folded ltr-image and the folded rtl-image are unfolded 104, 105 by way of a SENSE reconstruction that makes use of the coil sensitivity profiles 111. This SENSE reconstruction is known as such and usually employed for reconstruction of data that are undersampled in k-space in order to reduce the acquisition time of the data. From the unfolded ltr-image 104 and the unfolded rtl-image 105 the phase difference image 112 is derived. This phase difference image contains the phase differences of the ltr-data set relative the rtl-data set. These phase differences are built-up from differences between the phase encodings and differences between phase errors in the ltr-data set and the rtl-data set that caused by effects such as gradient switching delays, and eddy currents. Since the phase-encodings in the ltr-data set and in the rtl-data set are applied in a controlled manner, the spatial phase error distribution 113 can be derived from the phase difference image 112. To initialise the process, in the calibration stage 114 a first measurement of the spatial phase error distribution is measured by scanning two-dimensional k-space along a set of phase-encoding lines, where each line is scanned along opposite directions. The difference between the phase of the magnetic resonance signals acquired at opposite propagation directions represent the phase errors. Because the measurement is done at different phase-encoding values, the phase errors are measured in dependence of both the read-direction and the frequency encoding direction. This measured phase error distribution forms an initial estimate of the spatial phase error distribution. The phase error distribution may be obtained in various manners from the phase difference image, the measurement from the calibration stage and or the spatial phase error distribution 113 available from a previous iteration or from a previous dynamic. The phase error distribution could be simply replaced by the currently available phase difference image, but the current phase difference image may also be combined with the result from the calibration stage, from a previous dynamic or information retained. In this way account can be taken of a possibly higher noise level in the phase difference images as well as the result from the calibration stage becoming relatively outdated.

[0029] The diagnostic magnetic resonance image is reconstructed 106 on the basis of the spatial sensitivity profiles, the spatial phase error distribution and the global encoding relationship is established between the juxtaposed ltr-dataset and rtl-dataset and the (pixel-values of) the final magnetic resonance image. The pixel-values of the diagnostic magnetic resonance image can be employed for a regularisation approach in the unfolding (104, 105) of the rtl-folded image and the ltr-folded images. This regularisation improves the numerical stability of the unfolding of the rtl-folded image and the ltr-folded image and reduces the noise level in the unfolded images. Hence, the noise level in the phase-error distribution is reduced.

[0030] In the iterative approach, the diagnostic magnetic resonance image can be updated from time to time in successive iterations. Thus, at the current iteration, the regularisation can be done on relatively accurate pixel-values of the currently available version of the diagnostic magnetic resonance image which can be refreshed from time to time so as to account for the phase error distribution growing more accurate as the iterations progress.

[0031] Alternatively, in a dynamic approach (shown schematically by the dashed lines) successive single-shot EPI acquisitions are made. Thus, k-space acquisitions are done at successive instants in time, which then represent dynamic change that may occur in the object, such as due to movement caused by the patient's heartbeat and respiration. In such a dynamic approach, as an estimate of the phase error distribution, the result for the phase error distribution from an earlier, preferably the previous, dynamic may be employed. It appears that the phase error distribution only slowly varies over dynamics and it has also appeared in the iterative approach that often a single iteration is sufficient for an accurate determination of the phase error distribution.

[0032] In more mathematical detail, the reconstruction of the diagnostic magnetic resonance image from the single-shot EPI acquisition(s) is as follows. For the odd and even echoes (i.e. the ltr-dataset and the rtl-dataset) SENSE equations can be written as:

S.sub.even{right arrow over (p)}={right arrow over (m)}.sub.even S.sub.odd{right arrow over (p)}={right arrow over (m)}.sub.odd

[0033] S is the coil sensitivity matrix, m is the measured data and p the final image pixels of the unfolded ltr-image 104 and the unfolded rtl-image 105.

[0034] is a diagonal matrix containing the delta phase encoding .sub.enc and the 2D EPI phase errors .sub.epi:

[00003]$=\left(\begin{array}{ccc}{}^{\left({}_{\mathrm{enc}}\left(r_1\right)+{}_{\mathrm{epi}}\left(r_1\right)\right)}& 0& 0\\ 0& & 0\\ 0& 0& {}^{\left({}_{\mathrm{enc}}\left(r_N\right)+{}_{\mathrm{epi}}\left(r_N\right)\right)}\end{array}\right)$

[0035] With N=2*R, where R is the SENSE reduction factor, and 2 the extra SENSE factor by splitting the odd and even echoes. The sensitivity encoding, remaining phase encoding and phase errors can be combined in one sensitivity matrix S.sub.even and S.sub.odd.

S.sub.even=S.sub.even S.sub.odd=S.sub.odd

[0036] Let the even echoes contain the k=0 profile (so no delta phase encoding) and only a delta 2D EPI phase correction is applied to the odd echoes, now for the even and odd echoes is:

[00004]${}_{\mathrm{even}}=I,{}_{\mathrm{odd}}=\left(\begin{array}{ccc}{}^{\left({}_{\mathrm{enc}}\left(r_1\right)+{}_{\mathrm{epi}}\left(r_1\right)\right)}& 0& 0\\ 0& & 0\\ 0& 0& {}^{\left({}_{\mathrm{enc}}\left(r_N\right)+{}_{\mathrm{epi}}\left(r_N\right)\right)}\end{array}\right)$$\mathrm{with}.Math..Math.{}_{\mathrm{enc}}\left(r\right)=R.Math.\frac{2.Math.}{\mathrm{FOV}}.Math.r_{\mathrm{enc\_dir}}$

[0037] This .sub.enc is purposely introduced to have a better separation between the sets of equations; it is created by the k-space-distance between the odd and even k-space lines. The SENSE equation can now be written as:

S.sub.even{right arrow over (p)}=S{right arrow over (p)}={right arrow over (m)}.sub.even

S.sub.odd{right arrow over (p)}=S{right arrow over (p)}={right arrow over (m)}.sub.odd (S.sub.odd=S)

[0038] Combining the odd and even echoes in one so-called SENSE-IRIS reconstruction kernel:

[00005]$\left[\begin{array}{c}S\\ S^{}\end{array}\right].Math.\stackrel{->}{p}=\left[\begin{array}{c}{\stackrel{->}{m}}_{\mathrm{even}}\\ {\stackrel{->}{m}}_{\mathrm{odd}}\end{array}\right]->S_{\mathrm{all}}.Math.{\stackrel{->}{p}}_{\mathrm{all}}={\stackrel{->}{m}}_{\mathrm{all}}$

[0039] Where p.sub.all is the diagnostic magnetic resonance image resulting from odd-even echoes combined unfolding reconstruction including 2D EPI phase correction.

[0040] Now to determine the EPI phase changes over dynamics, the odd and even echoes can additionally be reconstructed separately. For example for the even echoes holds

S{right arrow over (p)}={right arrow over (m)}.sub.even+{right arrow over (n)}.sub.n N.sub.n=N(0, .sub.n)

{right arrow over (p)}={right arrow over (p)}.sub.all+{right arrow over (n)}.sub.p N.sub.p=N(0, f({right arrow over (p)}.sub.all))=N(0,R)

[0041] Here p.sub.all is used to regularize (R) the reconstruction. Function f needs to be tuned and instructs the SENSE reconstruction how close the solution is to the previous full solution (p.sub.all). The noise contribution is n.sub.n to the measured data. The reconstruction of the unfolded pixels may include reconstruction uncertainties and errors which is accounted for by the term n.sub.p. In a regularisation approach in the unfolding it is assumed that the unfolding solution is close to the reference p.sub.all. This reference can be obtained from a previous solution such as (1) the solution of the previous iteration or (2) the solution of the previous dynamic.

[0042] Regularisation matrix R typically depends on the modulus of p.sub.all:

[00006]$R^{-1/2}=F.Math.\left[\begin{array}{cc}.Math.{\stackrel{->}{p}}_{\mathrm{all},r_1}.Math.& 0\\ 0& .Math.{\stackrel{->}{p}}_{\mathrm{all},r_{\mathrm{Sf}}}.Math.\end{array}\right]$

[0043] The size of the matrix is equivalent to the number of SENSE folded pixels (Sf).

[0044] If the solution is expected to differ 10% from p.sub.all, F=0.1. If the previous dynamic is used for regularisation, and the expected changes (by heating) are small (e.g. 1%), F can be chosen smaller (e.g. 0.01). In an iterative reconstruction f can be reduced (stronger regularisation) for the higher iterations.

[0045] The SENSE solution for the even and odd echoes is:

[00007]${\stackrel{->}{p}}_{\mathrm{even}}={\left(S^H.Math.{}_n^{-1}.Math.S+R^{-1}\right)}^{-1}\left[S^H.Math.{}_n^{-1}.Math.R^{-1}\right]\left[\begin{array}{c}{\stackrel{->}{m}}_{\mathrm{even}}\\ {\stackrel{->}{p}}_{\mathrm{all}}\end{array}\right]$${\stackrel{->}{p}}_{\mathrm{odd}}={\left(S^{.Math..Math.H}.Math.{}_n^{-1}.Math.S^{}+R^{-1}\right)}^{-1}\left[S^{.Math..Math.H}.Math.{}_n^{-1}.Math.R^{-1}\right]\left[\begin{array}{c}{\stackrel{->}{m}}_{\mathrm{odd}}\\ {\stackrel{->}{p}}_{\mathrm{all}}\end{array}\right]$

[0046] The phase difference image is now calculated by a simple subtraction:

.sub.EPI=angle({right arrow over (p)}.sub.even)angle({right arrow over (p)}.sub.odd)

[0047] The separate SENSE reconstructions of the odd and even echoes result in lower SNR, due to higher SENSE geometry factors. So these images are not optimal for clinical use. But sufficient to determine a global 2D EPI phase change. For example fit .sub.EPI to a 2D linear phase error or strongly smooth the .sub.EN map.

[0048] The estimated EPI is added to the 2D EPI phase errors and used in the SENSE-IRIS reconstruction of the next dynamic, resulting in a dynamically updated 2D EPI phase correction, integrated in the SENSE reconstruction.

[0049] The FIG. 3 shows diagrammatically a magnetic resonance imaging system in which the invention is used. The magnetic resonance imaging system includes a set of main coils 10 whereby the steady, uniform magnetic field is generated. The main coils are constructed, for example in such a manner that they enclose a tunnel-shaped examination space. The patient to be examined is placed on a patient carrier which is slid into this tunnel-shaped examination space. The magnetic resonance imaging system also includes a number of gradient coils 11, 12 whereby magnetic fields exhibiting spatial variations, notably in the form of temporary gradients in individual directions, are generated so as to be superposed on the uniform magnetic field. The gradient coils 11, 12 are connected to a controllable power supply unit 21. the gradient coils 11, 12 are energised by application of an electric current by means of the power supply unit 21; to this end the power supply unit is fitted with electronic gradient amplification circuit that applies the electric current to the gradient coils so as to generate gradient pulses (also termed gradient waveforms) of appropriate temporal shape

[0050] The strength, direction and duration of the gradients are controlled by control of the power supply unit. The magnetic resonance imaging system also includes transmission and receiving coils 13, 16 for generating the RF excitation pulses and for picking up the magnetic resonance signals, respectively. The transmission coil 13 is preferably constructed as a body coil 13 whereby (a part of) the object to be examined can be enclosed. The body coil is usually arranged in the magnetic resonance imaging system in such a manner that the patient 30 to be examined is enclosed by the body coil 13 when he or she is arranged in the magnetic resonance imaging system. The body coil 13 acts as a transmission antenna for the transmission of the RF excitation pulses and RF refocusing pulses. Preferably, the body coil 13 involves a spatially uniform intensity distribution of the transmitted RF pulses (RFS). The same coil or antenna is usually used alternately as the transmission coil and the receiving coil. Furthermore, the transmission and receiving coil is usually shaped as a coil, but other geometries where the transmission and receiving coil acts as a transmission and receiving antenna for RF electromagnetic signals are also feasible. The transmission and receiving coil 13 is connected to an electronic transmission and receiving circuit 15.

[0051] It is to be noted that it is alternatively possible to use separate receiving and/or transmission coils 16. For example, surface coils 16 can be used as receiving and/or transmission coils. Such surface coils have a high sensitivity in a comparatively small volume. The receiving coils, such as the surface coils, are connected to a demodulator 24 and the received magnetic resonance signals (MS) are demodulated by means of the demodulator 24. The demodulated magnetic resonance signals (DMS) are applied to a reconstruction unit. The receiving coil is connected to a preamplifier 23. The preamplifier 23 amplifies the RF resonance signal (MS) received by the receiving coil 16 and the amplified RF resonance signal is applied to a demodulator 24. The demodulator 24 demodulates the amplified RF resonance signal. The demodulated resonance signal contains the actual information concerning the local spin densities in the part of the object to be imaged. Furthermore, the transmission and receiving circuit 15 is connected to a modulator 22. The modulator 22 and the transmission and receiving circuit 15 activate the transmission coil 13 so as to transmit the RF excitation and refocusing pulses. The reconstruction unit derives one or more image signals from the demodulated magnetic resonance signals (DMS), which image signals represent the image information of the imaged part of the object to be examined. The reconstruction unit 25 in practice is constructed preferably as a digital image processing unit 25 which is programmed so as to derive from the demodulated magnetic resonance signals the image signals which represent the image information of the part of the object to be imaged. The signal on the output of the reconstruction monitor 26, so that the monitor can display the magnetic resonance image. It is alternatively possible to store the signal from the reconstruction unit 25 in a buffer unit 27 while awaiting further processing.

[0052] The magnetic resonance imaging system according to the invention is also provided with a control unit 20, for example in the form of a computer which includes a (micro)processor. The control unit 20 controls the execution of the RF excitations and the application of the temporary gradient fields. To this end, the computer program according to the invention is loaded, for example, into the control unit 20 and the reconstruction unit 25.