METHOD AND APPARATUS FOR RECONSTRUCTION OF MAGNETIC RESONANCE IMAGES WITH INCOMPLETE SAMPLING

Abstract

A magnetic resonance (MR) image is created by executing an imaging sequence with an MR apparatus, wherein data in k-space are acquired using multiple receiving antennae, and reconstruction of all image points that correspond to all k-space points belonging to the imaging sequence takes place using a sensitivity profile of the receiving antennae in order to also take account of data at k-space points at positions at which no data were acquired. Data acquired at a number of positions of particular k-space points, the number of the particular k-space points being smaller than the number of all k-space points belonging to the imaging sequence. The aperture of each of the receiving antennae is configured such that, for acquisition of data at a respective k-space point, the spectral main lobe of the respective receiving antenna also extends over k-space points adjacent to the respective k-space point.

Claims

1. A method for generating a magnetic resonance (MR) image by executing an imaging sequence with a data acquisition scanner of a magnetic resonance apparatus, said method comprising: operating the data acquisition scanner to acquire MR data with a plurality of receiving antennae of the data acquisition scanner and entering the acquired MR data into a memory organized as k-space comprising a plurality of k-space points, with the acquired MR data being entered into k-space at respective positions of particular k-space points with a number of said particular k-space points being smaller than a number of all k-space points belonging to the imaging sequence; configuring an aperture of each of the receiving antennae to cause data to be acquired at a respective k-space point, with a spectral main lobe of each receiving antenna also extending over k-space points that are adjacent to the respective k-space point; and in an image reconstruction computer, reconstructing all image points that correspond to all of said k-space points, using respective sensitivity profiles of the receiving antennae to thereby take account of data from k-space points at positions at which no MR data were acquired.

2. A method as claimed in claim 1 comprising implementing said reconstruction based on, for acquisition of MR data at a position of a particular k-space point with the receiving antennae, data of k-space points situated adjacent to the particular k-space point are also acquired, in order to calculate said data of k-space points at said positions at which no MR data were acquired.

3. A method as claimed in claim 1 comprising: entering the acquired MR data into k-space along trajectories that extend radially through k-space; and acquiring data for each trajectory by radiating a respective radio-frequency (RF) excitation pulse for that respective trajectory.

4. A method as claimed in claim 1, comprising: implementing the reconstruction of all image points based on the following equation (1):
C.sub.l(k.sub.x,k.sub.y,k.sub.z)I(k.sub.x,k.sub.y,k.sub.z)=I.sub.l(k.sub.x,k.sub.y,k.sub.z),l=1 . . . N.sub.Ant  (1), wherein N.sub.Ant represents the number of receiving antennae, I.sub.l(k.sub.x, k.sub.y, k.sub.z) represents the data acquired at the sampling position (k.sub.x, k.sub.y, k.sub.z) by the l-th receiving antenna, C.sub.l(k.sub.x, k.sub.y, k.sub.z) represents the spectral sensitivity profile (64) of the l-th receiving antenna at the sampling position (k.sub.x, k.sub.y, k.sub.z), and I(k.sub.x, k.sub.y, k.sub.z) represents the data of the k-space point (k.sub.x, k.sub.y, k.sub.z).

5. A method as claimed in claim 4, comprising calculating the data I(k.sub.x, k.sub.y, k.sub.z) of each k-space point (k.sub.x, k.sub.y, k.sub.z) based on linear equations created for each sampling position (k.sub.x, k.sub.y, k.sub.z) according to the equation (1).

6. A method as claimed in claim 1, comprising: selecting the number of receiving antennae so as to satisfy the inequality N.sub.Ant≧1/(1−(N.sub.absent/N.sub.total)) wherein N.sub.Ant represents the number of receiving antennae, N.sub.absent represents the number of k-space points at positions at which no MR data were acquired, and N.sub.total represents the number of all k-space points.

7. A method as claimed in claim 1 comprising: determining the respective sensitivity profiles of the receiving antennae by: determining a distribution of electromagnetic properties in a volume portion from which the MR image is generated; calculating an absolute B1 map of the volume portion dependent on the electromagnetic properties in the volume portion and dependent on geometric dimensions and a position of each of the receiving antennae; and determining the sensitivity profiles dependent on the B1 map.

8. A method as claimed in claim 1 comprising determining the respective sensitivity profiles of the receiving antennae by: determining a relative spectral sensitivity for each of the receiving antennae; determining a distribution of electromagnetic properties in a volume portion from which the MR image is generated, dependent on the relative spectral sensitivities; and calculating the sensitivity profiles dependent on the electromagnetic properties, geometric properties, and a position of each of the receiving antennae, and dependent on the relative spectral sensitivities of the receiving antennae.

9. A method as claimed in claim 1 comprising: acquiring the MR data and entering the acquired MR data into the memory organized as k-space by radiating an RF excitation pulse in the data acquisition scanner, and acquiring the MR data after a first time following radiation of the RF excitation pulse; operating the data acquisition scanner to acquire further MR data, and entering the further MR data into k-space, after a second time following the RF excitation pulse that occurs after the first time, with said further data being acquired at each k-space point; calculating a sensitivity profile for each of the receiving antennae starting from the further MR data and from a partial coil image reconstructed from MR data respectively acquired by each of the receiving antennae; and reconstructing all of the image points using said calculated sensitivity profiles of the receiving antennae.

10. A method as claimed in claim 1 comprising, dependent on the respective apertures of the receiving antennae, determining a minimum spacing between k-space points in k-space at positions at which MR data must be acquired in order to be able to actually reconstruct all of the image points.

11. A method as claimed in claim 10 wherein said minimum spacing is defined as a product of n and Δk, wherein n is the largest natural number that fulfills the inequality n<1/(A.Math.Δk), wherein A is the aperture of the receiving antennae and Δk is the discretization interval.

12. A method as claimed in claim 1 comprising: dependent on the aperture of the receiving antennae, determining an underscanning rate at which k-space is underscanned; and making said underscanning rate proportional to a reciprocal of the aperture of the receiving antennae so that, despite said underscanning rate, all of the image points are reconstructed.

13. A method as claimed in claim 1 comprising calculating the aperture of at least one of said receiving antennae by determining a radius such that if, for each k-space point at a position at which said MR data are acquired, a sphere with said radius is constructed around the respective k-space point, then also the k-space points at positions at which no data are acquired also lie within at least one of said spheres, and calculating the aperture of the at least one receiving antenna dependent on said radius.

14. A method for calculating an aperture of a receiving antenna of a data acquisition scanner of a magnetic resonance apparatus used to acquire MR data that are entered into a memory organized as k-space at respective k-space points in k-space, by determining a radius such that if, for each k-space point at a position at which said MR data are acquired, a sphere with said radius is constructed around the respective k-space point, then also the k-space points at positions at which no data are acquired also lie within at least one of said spheres, and calculating the aperture of the at least one receiving antenna dependent on said radius.

15. A method as claimed in claim 14, comprising determining the radius by determining a number n of the k-space points that lie at the start or at the end of a trajectory in k-space and at the position of which no data are acquired, and multiplying the number n by the discretization interval Δk, and with the aperture A fulfilling the inequality A<1/(n.Math.Δk).

16. A method as claimed in claim 15 comprising acquiring said MR data with a receiving antenna comprising a circular loop, said loop having a radius that is not more than (1/n).Math.FOV, wherein FOV is a dimension of a field of view corresponding to k-space.

17. A method as claimed in claim 16 wherein said radius of said loop is a maximum radius for which said inequality is fulfilled.

18. A magnetic resonance (MR) apparatus comprising: an MR data acquisition scanner comprising a plurality of receiving antennae; a control computer configured to operate the data acquisition scanner to acquire MR data with a plurality of receiving antennae of the data acquisition scanner and entering the acquired MR data into a memory organized as k-space comprising a plurality of k-space points, with the acquired MR data being entered into k-space at respective positions of particular k-space points with a number of said particular k-space points being smaller than a number of all k-space points belonging to the imaging sequence; each of the receiving antennae having an aperture that causes data to be acquired at a respective k-space point, with a spectral main lobe of each receiving antenna also extending over k-space points that are adjacent to the respective k-space point; and an image reconstruction computer configured to reconstruct all image points that correspond to all of said k-space points, using respective sensitivity profiles of the receiving antennae to thereby take account of data from k-space points at positions at which no MR data were acquired.

19. A magnetic resonance (MR) apparatus comprising: an MR data acquisition scanner comprising a plurality of receiving antennae, with at least one of said receiving antennae having an aperture; and a computer configured to determine said aperture for said at least one of said receiving antennae by determining a radius such that it for each k-space point at a position at which said MR data are acquired, a sphere with said radius is constructed around the respective k-space point, then also the k-space points at positions at which no data are acquired also lie within at least one of said spheres, and calculating the aperture of the at least one receiving antenna dependent on said radius.

20. A computer for calculating an aperture of a receiving antenna of a data acquisition scanner of a magnetic resonance apparatus used to acquire MR data that are: entered into a memory organized as k-space at respective k-space points in k-space, said computer comprising a processor configured to determine a radius such that if, for each k-space point at a position at which said MR data are acquired, a sphere with said radius is constructed around the respective k-space point, then also the k-space points at positions at which no data are acquired also lie within at least one of said spheres, and to calculate the aperture of the at least one receiving antenna dependent on said radius; and an output interface at which said processor provides an electronic representation of the calculated aperture.

21. A computer as claimed in claim 20 wherein said processor is configured, starting from a set of receiving antennae, to determine a receiving antenna having an aperture that is smaller than a maximum aperture and that has a smallest difference from the maximum aperture within said set of receiving antennae.

22. A non-transitory, computer-readable data storage medium encoded with programming instructions, said storage medium being loaded into a computer system of a magnetic resonance (MR) apparatus comprising an MR data acquisition scanner having a plurality of receiving antennae, said programming instructions causing said computer system to: operate the data acquisition scanner to acquire MR data with a plurality of receiving antennae of the data acquisition scanner and entering the acquired MR data into a memory organized as k-space comprising a plurality of k-space points, with the acquired MR data being entered into k-space at respective positions of particular k-space points with a number of said particular k-space points being smaller than a number of all k-space points belonging to the imaging sequence; configure an aperture of each of the receiving antennae to cause data to be acquired at a respective k-space point, with a spectral main lobe of each receiving antenna also extending over k-space points that are adjacent to the respective k-space point; and reconstruct all image points that correspond to all of said k-space points, using respective sensitivity profiles of the receiving antennae to thereby take account of data from k-space points at positions at which no MR data were acquired.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0112] FIG. 1 shows the sequence for a ZTE MR method together with corresponding regions in k-space.

[0113] FIG. 2 shows a schematic representation of an inventive magnetic resonance apparatus.

[0114] FIG. 3 shows the relationship between the sensitivity of a receiving antenna in the image domain and in the spectral domain for a large receiving antenna.

[0115] FIG. 4 shows the relationship between the sensitivity of a receiving antenna in the image domain and in the spectral domain for a small receiving antenna.

[0116] FIG. 5 shows a comparison between a conventional sampling and an inventive sampling of k-space.

[0117] FIG. 6 shows a sequence diagram for an inventive embodiment.

[0118] FIG. 7 is a flow diagram of an inventive embodiment.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0119] FIG. 2 is a schematic illustration of an inventive magnetic resonance apparatus 5 (a magnetic resonance and/or nuclear spin tomography device). Herein, a basic field magnet 1 of the scanner of the apparatus generates a temporally constant, strong basic magnetic field for polarizing and aligning nuclear spins in an examination region of an object O, for example, a part of a human body to be investigated, who is examined lying on a table 23 in the scanner of the magnetic resonance apparatus 5. The high degree of homogeneity of the basic magnetic field required for magnetic resonance measurements is defined in a typically spherical measurement volume M in which the volume portion of the human body to be investigated is arranged. To support the homogeneity requirements and, in particular, to eliminate temporally invariable influences, “shim plates” made of ferromagnetic material are introduced at suitable sites. Temporally variable influences are eliminated by shim coils 2.

[0120] Inserted into the basic field magnet 1 is a cylindrical gradient coil system 3, composed of three sub-windings. Each sub-winding is supplied with current from an amplifier to generate a linear (also temporally variable) gradient field in the relevant direction of the Cartesian coordinate system. The first sub-winding of the gradient coil system 3 generates a gradient G.sub.x in the x-direction, the second sub-winding generates a gradient G.sub.y in the y-direction, and the third sub-winding generates a gradient G.sub.z in the z-direction. Each amplifier has a digital-analog converter, which is controlled by a sequence controller 18 for timely generation of gradient pulses.

[0121] Arranged within the gradient coil system 3 is one (or more) radio-frequency antennae 4 which convert the radio-frequency pulses emitted by a radio-frequency power amplifier into an alternating magnetic field for excitation of the nuclei and deflecting the nuclear spins of the object O under investigation or the region of the object O under investigation. Each radio-frequency antenna 4 has one or more RF transmitter coils and one or more RF receiving coils in the form of a ring-shaped, preferably linear or matrix-shaped arrangement of component coils. In addition, there are a number of relatively small receiving antennae 24, which have a small aperture. The alternating field emitted by the precessing nuclear spins, i.e. typically the nuclear spin echo signals evoked by a pulse sequence from one or more radio-frequency pulses and one or more gradient pulses, is also converted by the RF receiving coils of the respective radio-frequency antenna 4 and the receiving antennae 24 into a voltage (measurement signal), which is fed by an amplifier 7 to a radio-frequency receiving channel 8 of a radio-frequency system 22. The radio-frequency system 22, which is part of a control computer 10 of the magnetic resonance apparatus 5, also has a transmitting channel 9 in which the radio-frequency pulses for the excitation of the magnetic nuclear resonance are generated. The respective radio-frequency pulses are represented digitally in the sequence controller 18 as a sequence of complex numbers on the basis of a pulse sequence pre-determined by the system computer 20. This sequence of numbers is fed as a real part and an imaginary part, respectively, via inputs 12 to a digital-analog converter in the radio-frequency system 22, and are fed from there to a transmitting channel 9. In the transmitting channel 9, the pulse sequences are modulated onto a radio-frequency carrier signal, the base frequency of which corresponds to the resonance frequency of the nuclear spins in the measurement volume.

[0122] Switching from transmitting to receiving operation is performed by a transmit/receive switch (diplexer) 6. The RF transmitter coils of the radio-frequency antenna(e) 4 radiate(s) the radio-frequency pulses to excite the nuclear spins in the measurement volume M and resulting echo signals are sampled by the RF receiving coil(s). The corresponding magnetic resonance signals obtained are phase-sensitively demodulated in the receiving channel 8′ (first demodulator) of the radio-frequency system 22 to an intermediate frequency, digitized in the analog-digital converter (ADC) and omitted by the output 11. This signal is then demodulated to the frequency 0. The demodulation to the frequency 0 and the separation into real and imaginary parts takes place, following digitizing in the digital domain, in a second demodulator 8. With an image computer 17, an MR image is reconstructed from the measurement data obtained in this way from the output 11. The administration of the measurement data, the image data and the control programs is carried out by the system computer 20. From a specification with control programs, the sequence controller 18 controls the creation of the desired pulse sequences and the corresponding sampling of k-space. The sequence controller 18 controls the timely switching of the gradients, the emission of the radio-frequency pulses at a defined phase amplitude, and the reception of the magnetic resonance signals. The time base for the radio-frequency system 22 and the sequence controller 18 is made available by a synthesizer 19. The selection of corresponding control programs for generating an MR image which are stored, for example, on a DVD 21, and the representation of the generated MR image, is carried out via a terminal 13, which has a keyboard 15, a mouse 16 and a screen 14.

[0123] FIG. 3 shows, on the left side, an exemplary spatial sensitivity profile of a receiving antenna which has a spatial aperture (penetration depth), which approximately corresponds to ⅙ of the FOV. FIG. 3 shows the main lobe 61 in the spatial domain. The penetration depth corresponds to a region in which the spatial coil sensitivity does not fall substantially (i.e. the spatial coil sensitivity in this region never lies below a particular percentage (in particular 5%) of the maximum of the coil sensitivity in the image domain).

[0124] FIG. 3 shows, on the right side, the resultant spectral sensitivity profile of the same receiving antenna, which has a spectral footprint or a spectral main lobe 62 which approximately corresponds to 1/60 of the whole k-space. This corresponds to a k-space region in which the spectral sensitivity of the antenna does not fall substantially (i.e. the spectral sensitivity of the antenna in this region never lies below the pre-determined percentage (in particular 5%) of the maximum of the antenna sensitivity in k-space). If k-space covers, for example, 128×128 pixels, this means that such a receiving antenna acquires spectral energy mainly from a very small region round a single k-space point that extends essentially radially over less than one discretization interval Δk in k-space.

[0125] For comparison, FIG. 4 shows an exemplary spatial sensitivity profile of a receiving antenna that has a spatial aperture (penetration depth) that approximately corresponds to 1/60 of the FOV. FIG. 4 shows the main lobe 63 in the spatial domain. In this case, also, the penetration depth corresponds to a region in which the spatial sensitivity of the antenna does not fall substantially (i.e. the spatial sensitivity of the antenna in this region never lies below a pre-determined percentage of the maximum of the antenna sensitivity in the image domain).

[0126] As in FIG. 3, FIG. 4 shows, on the right side, the resultant spectral sensitivity profile of the same receiving antenna, which has a spectral footprint or a spectral main lobe 64 which approximately corresponds to ⅙ of the whole k-space. This corresponds to a k-space region in which the spectral sensitivity of the antenna does not fall substantially (i.e. the spectral sensitivity of the antenna in this region never lies below the pre-determined percentage (in particular 5%) of the maximum of the antenna sensitivity in the k-space). If k-space covers, for example 128×128 pixels, this means that such a receiving antenna acquires spectral energy mainly from a relatively large region that radially covers essentially 20 k-space points or discretization intervals Δk.

[0127] With conventional data acquisition with a magnetic resonance apparatus, essentially data are acquired only in the immediate vicinity of the k-space point at the position at which the data acquisition takes place. It is apparent from the extent of the main lobe 72 (at left in FIG. 5) that, due to the sharply focused spectral sensitivity of a large receiving antenna, for each data acquisition at a particular k-space point, only the data of this particular k-space point 75 are acquired, since the sensitivity profile of the conventional receiving antenna does not extend over the k-space points adjacent to this particular k-space point. For sampling along the k-space rows 71, therefore (almost) only the data of the k-space points 74 lying on the k-space rows 71 are acquired.

[0128] In contrast thereto, with the inventive data acquisition, the data are acquired with a receiving antenna of relatively small aperture. If, in a similar way as shown at left in FIG. 5 for the conventional case, data are acquired for the k-space point 75, at the position k.sub.x=3, k.sub.y=2 with the smaller receiving antenna, due to the relatively larger main lobe 73 of the smaller receiving antenna, data are also acquired in a radius of 4×Δk round the position k.sub.x=3, k.sub.y=2, so that data are acquired from numerous adjacent k-space points 74.

[0129] FIG. 6 shows an inventive sequence diagram. Before the RF excitation pulse 41 is radiated, the gradients 42 are ramped up. A first data acquisition, wherein a free induction signal 45 is acquired, takes place after as short a dead time 82 as possible. This first data acquisition takes place along radial trajectories with which, due to the unavoidable dead time 82, data cannot be acquired from the region of the k-space center.

[0130] Following the first readout time 44 after the first data acquisition, further gradients 42 are switched (activated) in order to generate a gradient echo 81, which is acquired at a further readout time 44. The data acquired during the second data acquisition are used to determine or calibrate the spectral sensitivity profiles of the receiving antennae. These determined sensitivity profiles of the receiving antennae are used, in order, in the reconstruction of an MR image from the first data, also to take account of or determine the data of those k-space points in the center.

[0131] Furthermore, on the basis of the second data, a further MR image can be reconstructed.

[0132] FIG. 7 shows a flow diagram of an inventive embodiment.

[0133] In the first step S1, data are acquired at particular k-space points respectively by a number of receiving antennae. In the second step S2, the sensitivity profiles of the receiving antennae are determined. The receiving antennae are configured such that the main lobe of each receiving antenna also extends, when data are acquired at the position of a particular k-space point, over adjacent k-space points.

[0134] Since the main lobe of each receiving antenna also extends over adjacent k-space points, in step S3, the data of all k-space points can be calculated on the basis of linear equations. Herein, for each k-space point at a position at which data were acquired, and for each receiving antenna, a respective linear equation can be created so as to also calculate the data for those k-space points at positions at which no data were acquired.

[0135] Lastly, in step S4, the reconstruction of all image points takes place.

[0136] Although modifications and changes may be suggested by those skilled in the art, it is the intention of the Applicant to embody within the patent warranted hereon all changes and modifications as reasonably and properly come within the scope of the Applicant's contribution to the art.