Patent Description:
A large static magnetic field is used by Magnetic Resonance Imaging (MRI) scanners to align the nuclear spins of atoms as part of the procedure for producing images within the body of a patient. This large static magnetic field is referred to as the B0 field or the main magnetic field. Various quantities or properties of the subject can be measured spatially using MRI. For example, various electrical properties of a subject can be investigated using MRI. Gradient echo magnetic resonance imaging is a commonly used method commonly used for rapidly acquiring magnetic resonance imaging data. It is commonly used for three-dimensional imaging.

United States patent <CIT> discloses a method of shimming an NMR magnet uses a plurality of 1D projections through a sample volume to determine the inhomogeneities of the field of the NMR magnet. The frequency distributions obtained are assembled from the phase signals of the various projections. In order to avoid frequency errors due to phase wrapping, the phase of each signal is monitored over time for discontinuities indicative of aliasing. For each phase wrap, the signal is "unwrapped" by adjusting the value of the phase signal by 2π. The same method is used to establish a shim field map for each of the shim coils being used. With one shim coil at a time being driven with a predetermined current, the detection method is repeated to acquire a shim-base frequency map for each shim coil. The base frequency map is then subtracted from the shim-base frequency maps to obtain shim field maps. The proper shim currents are then acquired through matrix operations on the shim field maps and the base frequency map.

<NPL>, discloses a method to estimate B0-fluctuations based on the analysis of raw-k-pace data, without sequence modifications or external hardware and correct for their detrimental effects in gradient-echo MRI.

The invention provides for a medical system, a computer program, and a method in the independent claims. Embodiments are given in the dependent claims.

A difficulty with gradient echo magnetic resonance imaging is that inhomogeneities in the B0 field, also known as off-resonance effects, can cause signal voids. Embodiments may provide for a means of reducing signal voids due to off-resonance effects. This may be achieved by a process of upsampling an initial magnetization image and upsampling an off-resonance phase map. The initial magnetization image is reconstructed from measured gradient echo k-space data. A modulated image is then calculated by modulating the upsampled image with the upsampled off-resonance phase map. This modulated image is then used in an iterative scheme that uses data consistency with the measured gradient echo k-space data as well as demodulation by the upsampled off-resonance phase map to calculate an updated image. Several algorithms are described below.

In one aspect the invention providesfera medical system in accordance with claim <NUM> that comprises a memory storing machine-executable instructions. The medical system further comprises a processor configured for executing the machine-executable instructions and for controlling the medical system. Execution of the machine-executable instructions causes the processor to receive measured gradient echo k-space data. In magnetic resonance imaging data is acquired in k-space and then later reconstructed using Fourier transforms into image space.

The measured gradient echo k-space data is k-space data that has been acquired with a gradient echo magnetic resonance imaging protocol. Execution of the machine-executable instructions further causes the processor to receive an off-resonance phase map. An off-resonance phase map is a mapping of the off-resonance frequency for each voxel. It may for example be a B0 map that has been multiplied with the echo time of the gradient echo magnetic resonance imaging protocol used to measure the gradient echo k-space data. The off-resonance phase map may for example be received in the form of the actual off-resonance phase map or it may also be a B0 map which may be used to calculate the off-resonance phase map.

Execution of the machine-executable instructions further causes the processor to reconstruct an initial magnetization image from the measured gradient echo k-space data. In this step the measured gradient echo k-space data is used to reconstruct a magnetic resonance image in image space, herein referred to as the initial magnetization image.

In later steps the image will be corrected and refined. However, at this step an image is reconstructed without this correction. Execution of the machine-executable instructions further causes the processor to calculate an upsampled phase map from the off-resonance phase map. For the upsampled phase map and the later mentioned upsampled image an upsampled resolution is chosen. The upsampled phase map may for example be calculated by interpolating the off-resonance phase map for this higher resolution. Execution of the machine-executable instructions further causes the processor to calculate an upsampled image from the initial magnetization image. In this case the initial magnetization image is upsampled. This for example may also be through an interpolation process.

Execution of the machine-executable instructions further causes the processor to calculate a modulated image by modulating the upsampled image with the upsampled phase map. The modulated image is then affected by the upsampled phase map at a higher resolution than the initial magnetization image. The following steps are then performed iteratively to calculate a corrected image. First, updated k-space data is calculated by applying a data consistency algorithm to a k-space representation of the modulated image and the measured gradient echo k-space data. For example, the modulated image may be represented in k-space. This is the k-space representation. However, there is still the measured gradient echo k-space data. The application of the data consistency algorithm ensures that the k-space representation of the modulated image is adjusted so that it better fits the actually measured gradient echo k-space data.

In the next iterative step, the updated image is calculated from the updated k-space date. The calculation of the updated image comprises demodulation by the upsampled phase map. The calculating of the updated image further comprises applying a smoothing algorithm. The modulated image for further iterations results from the updated image.

This embodiment may have the advantage that it provides for a means of reducing the effect of phase modulation within individual voxels. It is done in an iterative fashion and the corrected image is gradually improved.

As will be described below there are several different approaches in which this algorithm can be applied. In one approach the image is downsampled and upsampled for every iteration and a de-ringing algorithm or equivalent operation is applied. In another approach, during each duration a residual is calculated which is used to update the modulated image for each iteration. This algorithm resembles a compressed sensing type algorithm.

In another embodiment the step of calculating the modulated image by modulating the upsampled image by the upsampled phase map is performed iteratively during the iterative calculation of the corrected image. The calculation of the updated image from the updated k-space comprises calculating an intermediate image from the updated k-space data. The calculation of the updated image from the updated k-space further comprises calculating a demodulated image by demodulating the intermediate image with the upsampled phase map. The calculation of the updated image from the updated k-space data further comprises calculating the updated image from the demodulated image. The updated image is either output as a corrected image or used as the upsampled image in a further iteration.

The computations of the magnetic resonance images from the MR data sampled from k-space may be done by reconstruction software installed on a host computer of the magnetic resonance examination system. Alternatively, reconstruction may be done remotely separated in time and place form the magnetic resonance examination system and the MR data acquisition e.g. by uploading the gradient echo k-space data and the off-resonance phase map to 'the cloud' where correction and reconstructing may be done by dedicated correction and reconstruction software.

In another embodiment the updated image is calculated by applying a spatial smoothing filter to the demodulated image. For example, the downsampling at the end of each iteration may be performed by performing a smoothing operation.

In another embodiment the updated image is calculated by calculating demodulated k-space data from the demodulated image. The updated image is further calculated by calculating the updated image by applying a k-space mask to the demodulated k-space data and applying a de-ringing filter to the demodulated k-space data.

In another embodiment the data consistency algorithm is configured to calculate the updated k-space data using a fitting of the k-space representation of the modulated image to the measured gradient echo k-space data. In this case the k-space data that is in a vicinity of the actual measured data may be adjusted so that it better fits.

In another embodiment the data consistency algorithm is configured to calculate the updated k-space data by replacing a portion of the k-space representation of the modulated image with the measured gradient echo k-space data. There may be particular regions or lines of k-space data that have been acquired. K-space data that is within the vicinity of this may be removed from the k-space representation of the modulated image and replaced with the actual measured k-space data.

In another embodiment the updated k-space data results from a calculation of a residual between a projection of the modulated image into Fourier space and the measured gradient echo k-space data. The calculation of the updated image from the updated k-space data then comprises calculating a residual image by transforming the residual to image space. The calculation of the updated image from the updated k-space data then further comprises calculating a demodulated residual image by demodulating the residual image with the upsampled phase map. The calculation of the updated image from the updated k-space data then further comprises updating the modulated image with the demodulated residual image. The residual for example may be added to the modulated image. After this then the iterations will start over again.

In another embodiment the smoothing algorithm is a regularization term applied during the updating of the modulated image with the demodulated residual image. The regularization term has a smoothing effect on the data and in some cases may be equivalent to the spatial smoothing filter or the de-ringing filter in k-space.

In another embodiment the measured gradient echo k-space data is parallel imaging magnetic resonance imaging data that was acquired according to a parallel imaging magnetic resonance imaging protocol from multiple antenna elements. The initial magnetization image is reconstructed according to the parallel imaging magnetic resonance imaging protocol. The data consistency algorithm is configured to modify the k-space data representation of the modulated image with the measured gradient echo k-space data from each of the multiple antenna elements collectively. This embodiment may be beneficial because it may provide for a means of proving parallel imaging gradient echo images.

In another embodiment the off-resonance phase map is received as a B0 inhomogeneity map. Execution of the machine-executable instructions further causes the processor to calculate the off-resonance phase map from the B0 inhomogeneity map. For example, the off-resonance phase map may be calculated by multiplying the B0 inhomogeneity map with the echo time.

In another embodiment the medical system further comprises a magnetic resonance imaging system. The memory further contains pulse sequence commands configured for controlling the magnetic resonance imaging system to acquire the measured gradient echo k-space data according to the gradient echo magnetic resonance imaging protocol. Execution of the machine-executable instructions further causes the processor to control the magnetic resonance imaging system with the pulse sequence commands to acquire the measured gradient echo k-space data.

In another aspect the invention provides a computer program in accordance with claim <NUM> that comprises machine-executable instructions for execution by a processor controlling a medical system. This may for example be a computer program product stored on a data carrier or transitory data storage medium. The execution of the machine-executable instructions causes the processor to receive measured gradient echo k-space data. Execution of the machine-executable instructions further causes the processor to receive an off-resonance phase map. Execution of the machine-executable instructions further causes the processor to reconstruct an initial magnetization image from the measured gradient echo k-space data.

Execution of the machine-executable instructions further causes the processor to calculate an upsampled phase map from the off-resonance phase map. Execution of the machine-executable instructions further causes the processor to calculate an upsampled image from the initial magnetization image. Execution of the machine-executable instructions further causes the processor to calculate a modulated image by modulating the upsampled image with the upsampled phase map. Execution of the machine-executable instructions further causes the processor to calculate a corrected image iteratively.

These iterative steps comprise calculating an updated k-space data by applying a data consistency algorithm to a k-space representation of the modulated image and the measured gradient echo k-space data. The iterative steps further comprise calculating an updated image from the updated k-space data. The calculation of the updated image comprises demodulation by the upsampled image. Calculating the updated image further comprises applying a smoothing algorithm. The modulated image for further iterations results from the updated image.

In another embodiment the step of calculating the modulated image by modulating the upsampled image by the upsampled phase map is performed iteratively during the iterative calculation of the corrected image. The calculation of the updated image from the updated k-space data comprises calculating an intermediate image from the updated k-space data. The calculation of the updated image from the updated k-space data further comprises calculating a demodulated image by demodulating the intermediate image with the upsampled phase map. The calculation of the updated image from the updated k-space data further comprises calculating the updated image from the demodulated image. The updated image is either output as the corrected image or used as the upsampled image in a further iteration.

In another embodiment the updated k-space data results from a calculation of a residual between a projection of the modulated image into Fourier space and the measured gradient echo k-space data. The calculation of the updated image from the updated k-space data comprises calculating a residual image by transforming the residual to image space. Calculating the updated image from the updated k-space further comprises calculating a demodulated residual image by demodulating the residual image with the upsampled phase map. Calculating the updated image from the updated k-space data further comprises updating the modulated image with the demodulated residual image.

In another embodiment, the measured gradient echo k-space data is received for one or more gradient echoes. The upsampled image is an upsampled magnetization image.

In another embodiment, the initial magnetization image is reconstructed for each of the one or more gradient echoes from the measured gradient echo k-space data. The upsampled magnetization image is calculated for each of the one or more gradient echoes from the initial magnetization image for each of the one or more gradient echoes. The modulated image is calculated for each of the one or more gradient echoes by modulating the upsampled image for each of the one or more gradient echoes with the upsampled phase map corresponding to the echo time of the respective gradient echo. The corrected image for each of the one or more gradient echoes is calculated iteratively. The updated k-space data is calculated by applying the data consistency algorithm to the k-space representation of the modulated image for each of the one or more gradient echoes and the measured gradient echo k-space data. The update image is calculated for each of the one or more gradient echoes from the updated k-space data.

In another embodiment, the initial magnetization image is calculated using a signal model dependent upon one or more parameter mappings. The iterative calculation of the corrected image comprises updating the parameter mappings.

In another embodiment, the signal model is a Dixon model.

In another embodiment, the signal model is an R2* mapping.

In another embodiment, the signal model is a parameter mapping model.

In another aspect the invention provides a method of operating a medical system in accordance with claim <NUM>.

The method comprises receiving measured gradient echo k-space data. The method further comprises receiving an off-resonance phase map. The method further comprises reconstructing an initial magnetization image from the measured gradient echo k-space data. The method further comprises calculating an upsampled phase map from the off-resonance phase map. The method further comprises calculating an upsampled image from the initial magnetization image. The method further comprises calculating a modulated image by modulating the upsampled image with the upsampled phase map. The method further comprises calculating a corrected image iteratively. The iterative calculation of the corrected image comprises calculating updated k-space data by applying a data consistency algorithm to a k-space representation of the modulated image and the measured gradient echo k-space data.

The calculation of the corrected image iteratively further comprises calculating an updated image from the updated k-space data. The calculation of the updated image comprises demodulation by the upsampled phase map. The calculation of the updated image further comprises applying a smoothing algorithm. The upsampled image for further iterations results from the updated image.

As will be appreciated by one skilled in the art, aspects of the present invention may be embodied as a apparatus, method, computer program or computer program product. " Furthermore, aspects of the present invention may take the form of a computer program product embodied in one or more computer readable medium(s) having computer executable code embodied thereon. A computer program comprises the computer executable code or "program instructions".

A 'computer-readable storage medium' as used herein encompasses any tangible storage medium which may store instructions which are executable by a processor of a computing device. The computer-readable storage medium may be referred to as a computer-readable non-transitory storage medium. The computer-readable storage medium may also be referred to as a tangible computer readable medium. In some embodiments, a computer-readable storage medium may also be able to store data which is able to be accessed by the processor of the computing device. Examples of computer-readable storage media include, but are not limited to: a floppy disk, a magnetic hard disk drive, a solid state hard disk, flash memory, a USB thumb drive, Random Access Memory (RAM), Read Only Memory (ROM), an optical disk, a magneto-optical disk, and the register file of the processor. Examples of optical disks include Compact Disks (CD) and Digital Versatile Disks (DVD), for example CD-ROM, CD-RW, CD-R, DVD-ROM, DVD-RW, or DVD-R disks. The term computer readable-storage medium also refers to various types of recording media capable of being accessed by the computer device via a network or communication link. For example a data may be retrieved over a modem, over the internet, or over a local area network. Computer executable code embodied on a computer readable medium may be transmitted using any appropriate medium, including but not limited to wireless, wireline, optical fiber cable, RF, etc., or any suitable combination of the foregoing.

'Computer memory' or 'memory' is an example of a computer-readable storage medium. Computer memory is any memory which is directly accessible to a processor. 'Computer storage' or 'storage' is a further example of a computer-readable storage medium. Computer storage is any non-volatile computer-readable storage medium. In some embodiments computer storage may also be computer memory or vice versa.

A 'processor' as used herein encompasses an electronic component which is able to execute a program or machine executable instruction or computer executable code. References to the computing device comprising "a processor" should be interpreted as possibly containing more than one processor or processing core. The processor may for instance be a multi-core processor. A processor may also refer to a collection of processors within a single computer system or distributed amongst multiple computer systems. The term computing device should also be interpreted to possibly refer to a collection or network of computing devices each comprising a processor or processors. The computer executable code may be executed by multiple processors that may be within the same computing device or which may even be distributed across multiple computing devices.

Computer executable code may comprise machine executable instructions or a program which causes a processor to perform an aspect of the present invention. Computer executable code for carrying out operations for aspects of the present invention may be written in any combination of one or more programming languages, including an object oriented programming language such as Java, Smalltalk, C++ or the like and conventional procedural programming languages, such as the "C" programming language or similar programming languages and compiled into machine executable instructions. In some instances the computer executable code may be in the form of a high level language or in a pre-compiled form and be used in conjunction with an interpreter which generates the machine executable instructions on the fly.

Generally, the program instructions can be executed on one processor or on several processors. In the case of multiple processors, they can be distributed over several different entities like clients, servers etc. Each processor could execute a portion of the instructions intended for that entity. Thus, when referring to a system or process involving multiple entities, the computer program or program instructions are understood to be adapted to be executed by a processor associated or related to the respective entity.

Aspects of the present invention are described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the invention. It will be understood that each block or a portion of the blocks of the flowchart, illustrations, and/or block diagrams, can be implemented by computer program instructions in form of computer executable code when applicable. It is further under stood that, when not mutually exclusive, combinations of blocks in different flowcharts, illustrations, and/or block diagrams may be combined.

A 'user interface' as used herein is an interface which allows a user or operator to interact with a computer or computer system. A 'user interface' may also be referred to as a 'human interface device. ' A user interface may provide information or data to the operator and/or receive information or data from the operator. A user interface may enable input from an operator to be received by the computer and may provide output to the user from the computer. In other words, the user interface may allow an operator to control or manipulate a computer and the interface may allow the computer indicate the effects of the operator's control or manipulation. The display of data or information on a display or a graphical user interface is an example of providing information to an operator. The receiving of data through a keyboard, mouse, trackball, touchpad, pointing stick, graphics tablet, joystick, gamepad, webcam, headset, pedals, wired glove, remote control, and accelerometer are all examples of user interface components which enable the receiving of information or data from an operator.

A 'hardware interface' as used herein encompasses an interface which enables the processor of a computer system to interact with and/or control an external computing device and/or apparatus. A hardware interface may allow a processor to send control signals or instructions to an external computing device and/or apparatus. A hardware interface may also enable a processor to exchange data with an external computing device and/or apparatus. Examples of a hardware interface include, but are not limited to: a universal serial bus, IEEE <NUM> port, parallel port, IEEE <NUM> port, serial port, RS-<NUM> port, IEEE-<NUM> port, Bluetooth connection, Wireless local area network connection, TCP/IP connection, Ethernet connection, control voltage interface, MIDI interface, analog input interface, and digital input interface.

A 'display' or 'display device' as used herein encompasses an output device or a user interface adapted for displaying images or data. A display may output visual, audio, and or tactile data. Examples of a display include, but are not limited to: a computer monitor, a television screen, a touch screen, tactile electronic display, Braille screen,.

Cathode ray tube (CRT), Storage tube, Bi-stable display, Electronic paper, Vector display, Flat panel display, Vacuum fluorescent display (VF), Light-emitting diode (LED) displays, Electroluminescent display (ELD), Plasma display panels (PDP), Liquid crystal display (LCD), Organic light-emitting diode displays (OLED), a projector, and Head-mounted display.

K-space data is defined herein as being the recorded measurements of radio frequency signals emitted by atomic spins using the antenna of a Magnetic resonance apparatus during a magnetic resonance imaging scan. K-space data is an example of medical image data. A Magnetic Resonance Imaging (MRI) image or MR image is defined herein as being the reconstructed two- or three-dimensional visualization of anatomic data contained within the magnetic resonance imaging data. This visualization can be performed using a computer.

<FIG> illustrates an example of a medical system <NUM>. The medical system <NUM> is shown as comprising a computer <NUM>. The computer <NUM> is intended to represent one or more computers or computer systems. The medical system <NUM> may take different forms in different examples. In one example the computer <NUM> could be a remote or cloud computing system that provides computational or image processing services. In another example the computer <NUM> could be part of a magnetic resonance imaging system. In yet other examples the computer <NUM> could be a workstation that is located at a radiology department or other location for healthcare professionals.

The computer <NUM> is shown as comprising a processor <NUM>. The processor <NUM> is intended to represent one or more processors that may be contained within one or more computers. The processors <NUM> may also be multiple computing cores. The processor <NUM> is shown as being connected to an optional hardware interface <NUM>. The hardware interface <NUM> may for example provide an interface which enables the processor <NUM> to control other components of the medical system <NUM>. For example, if the medical system <NUM> comprises a magnetic resonance imaging system, then the hardware interface <NUM> may be used by the processor <NUM> to control the magnetic resonance imaging system.

The computer <NUM> is further shown as containing an optional user interface <NUM>. For example, if the computer <NUM> is a computer that controls or does image reconstruction for a magnetic resonance imaging system the user interface <NUM> may provide for a means of an operator to interact with and control the medical system <NUM>. The processor <NUM> is further shown as being connected to a memory <NUM>. The memory <NUM> is intended to represent any memory that may be accessible to the processor <NUM>. This for example may be a non-transitory storage medium, a hard drive, or other storage medium.

The memory <NUM> is shown as containing machine-executable instructions <NUM>. The machine-executable instructions <NUM> contain instructions which enable the processor <NUM> to in some instances control the rest of the medical system <NUM> as well as perform various data and image processing tasks.

The memory <NUM> is further shown as containing measured gradient echo k-space data <NUM>. The measured gradient echo k-space data <NUM> is k-space data that has been acquired according to a gradient echo magnetic resonance imaging protocol. The memory <NUM> is further shown as containing an off-resonance phase map. The off-resonance phase map <NUM> may be received with the measured gradient echo k-space data <NUM>. For example, a B0 map may be measured at the same time as the measured gradient echo k-space data or before or afterwards and then used to calculate the off-resonance phase map <NUM>. The memory <NUM> is further shown as containing an initial magnetization image <NUM> that has been reconstructed from the measured gradient echo k-space data <NUM>. It should be noted that in some cases the measured gradient echo k-space data <NUM> may be parallel imaging k-space data. In which case there may be k-space data which is acquired for more than one coil element and the initial magnetization image <NUM> may be reconstructed using a coil sensitivity map.

The memory <NUM> is further shown as containing an upsampled phase map <NUM> and an upsampled image <NUM>. The upsampled phase map <NUM> and the upsampled image <NUM> have a resolution that is higher than the initial image <NUM>. Additionally, the upsampled phase map <NUM> and the upsampled image <NUM> have a chosen resolution that is the same for the both. The memory <NUM> is further shown as containing a modulated image <NUM>. The modulated image <NUM> is constructed by modulating the upsampled image <NUM> with the upsampled phase map <NUM>. The memory <NUM> is further shown as containing a corrected image <NUM> that has been calculated iteratively using the modulated image <NUM>.

The memory <NUM> is further shown as containing a corrected image <NUM> and updated k-space data <NUM>. The updated k-space data <NUM> is calculated using a data consistency algorithm <NUM> to compare a k-space representation <NUM> of the modulated image <NUM> with the measured gradient echo k-space data <NUM>. The memory <NUM> is further shown as containing an updated image <NUM> that is calculated by demodulation by the upsampled phase map. A smoothing algorithm <NUM> is used in calculating the updated image <NUM>. The modulated image <NUM> for further iterations is calculated or results from the updated image <NUM>.

<FIG> shows a flowchart which illustrates a method of operating the medical system of <FIG>. First, in step <NUM>, the measured gradient echo k-space data <NUM> is received. Next, in step <NUM>, the off-resonance phase map <NUM> is received. In step <NUM>, the initial image <NUM> is reconstructed from the measured gradient echo k-space data <NUM>. In step <NUM>, the upsampled phase map is calculated from the off-resonance phase map <NUM>. This for example may be calculated via interpolation. Next, in step <NUM>, the upsampled image <NUM> is calculated from the initial image <NUM>. This may also be calculated via interpolation. The size of the voxels in the upsampled phase map <NUM> and the upsampled image <NUM> is the same.

Next, in step <NUM>, the modulated image <NUM> is calculated by modulating the upsampled image <NUM> with the upsampled phase map <NUM>. Next, in step <NUM>, the corrected image <NUM> is calculated iteratively. Steps <NUM> and <NUM> represent some of the iterative steps. In step <NUM> the updated k-space data <NUM> is calculated by applying a data consistency algorithm <NUM> to a k-space representation <NUM> of the modulated image <NUM> and the measured gradient echo k-space data <NUM>. In step <NUM> the updated image <NUM> is calculated from the updated k-space data <NUM>.

The calculation of the updated image <NUM> comprises demodulation by the upsampled phase map <NUM>. When calculating the updated image further comprises applying a smoothing algorithm <NUM>. The modulated image for further iterations results from the updated image <NUM>. In some cases, the updated image replaces the modulated image. In other cases, the updated image is a residual which is used to update the modulated image.

<FIG> illustrates a further example of a medical system <NUM>. The medical system of <FIG> is similar to the medical system <NUM> of <FIG> except the medical system additionally comprises a magnetic resonance imaging system <NUM>.

The magnetic resonance imaging system <NUM> comprises a magnet <NUM>. The magnet <NUM> is a superconducting cylindrical type magnet with a bore <NUM> through it. The use of different types of magnets is also possible; for instance it is also possible to use both a split cylindrical magnet and a so called open magnet. A split cylindrical magnet is similar to a standard cylindrical magnet, except that the cryostat has been split into two sections to allow access to the iso-plane of the magnet, such magnets may for instance be used in conjunction with charged particle beam therapy. An open magnet has two magnet sections, one above the other with a space in-between that is large enough to receive a subject: the arrangement of the two sections area similar to that of a Helmholtz coil. Open magnets are popular, because the subject is less confined. Inside the cryostat of the cylindrical magnet there is a collection of superconducting coils.

Within the bore <NUM> of the cylindrical magnet <NUM> there is an imaging zone <NUM> where the magnetic field is strong and uniform enough to perform magnetic resonance imaging. A region of interest <NUM> is shown within the imaging zone <NUM>. A subject <NUM> is shown as being supported by a subject support <NUM> such that at least a portion of the subject <NUM> is within the imaging zone <NUM> and the region of interest <NUM>.

Within the bore <NUM> of the magnet there is also a set of magnetic field gradient coils <NUM> which is used for acquisition of preliminary magnetic resonance data to spatially encode magnetic spins within the imaging zone <NUM> of the magnet <NUM>. The magnetic field gradient coils <NUM> connected to a magnetic field gradient coil power supply <NUM>. The magnetic field gradient coils <NUM> are intended to be representative. Typically magnetic field gradient coils <NUM> contain three separate sets of coils for spatially encoding in three orthogonal spatial directions. A magnetic field gradient power supply supplies current to the magnetic field gradient coils. The current supplied to the magnetic field gradient coils <NUM> is controlled as a function of time and may be ramped or pulsed.

Adjacent to the imaging zone <NUM> is a radio-frequency coil <NUM> for manipulating the orientations of magnetic spins within the imaging zone <NUM> and for receiving radio transmissions from spins also within the imaging zone <NUM>. The radio frequency antenna may contain multiple coil elements. The radio frequency antenna may also be referred to as a channel or antenna. The radio-frequency coil <NUM> is connected to a radio frequency transceiver <NUM>. The radio-frequency coil <NUM> and radio frequency transceiver <NUM> may be replaced by separate transmit and receive coils and a separate transmitter and receiver. It is understood that the radio-frequency coil <NUM> and the radio frequency transceiver <NUM> are representative.

The radio-frequency coil <NUM> is intended to also represent a dedicated transmit antenna and a dedicated receive antenna. Likewise the transceiver <NUM> may also represent a separate transmitter and receivers. The radio-frequency coil <NUM> may also have multiple receive/transmit elements and the radio frequency transceiver <NUM> may have multiple receive/transmit channels. For example if a parallel imaging technique such as SENSE is performed, the radio-frequency could <NUM> will have multiple coil elements.

The transceiver <NUM> and the gradient controller <NUM> are shown as being connected to the hardware interface <NUM> of a computer system <NUM>.

The memory <NUM> is additionally shown as comprising pulse sequence commands <NUM>. The pulse sequence commands <NUM> are configured to acquire the measured gradient echo k-space data <NUM> according to a gradient echo magnetic resonance imaging protocol.

<FIG> shows a flowchart which illustrates a method of operating the medical system <NUM> of <FIG>. The method illustrated in <FIG> is similar to that shown in <FIG>. The method starts with step <NUM>. In step <NUM> the magnetic resonance imaging system <NUM> is controlled with the pulse sequence commands to acquire the measured gradient echo k-space data <NUM>.

An image reconstruction method is disclosed which reduces signal voids in gradient echo MR images which are caused by off-resonances in the imaged object. It also improves the quantitative accuracy of R2* maps. The new method is compatible with application of anti-ringing filters and potentially faster than other published methods with the same aim.

In MRI, an image is reconstructed from a set of sampled k-space data (e.g. by simple Fourier-transform for the case of regular Cartesian sampling). Since only a limited range in k-space is sampled, the reconstructed image may show some ringing at strong edges of the imaged object. To reduce ringing, it is common to apply a filter in k-space which reduces the amplitude of the ringing artefact. There are many anti-ringing filter shapes but all have in common that they attenuate signal for large values of |k|.

Gradient echo sequences are susceptible to local variations of the magnetic field (off-resonance). Common gradient echo image artefacts that are caused by off-resonances include geometric distortion, signal inhomogeneity (ripple or ringing-like structures) and signal voids. Signal voids occur in those location in the image where the gradient of the off-resonance is large because this leads to intra-voxel dephasing.

<FIG>, and <FIG> shows that applying an anti-ringing filter can increase off-resonance artefacts in gradient echo scans. <FIG> and <FIG> illustrate the benefit of some examples which construct a corrected image iteratively. <FIG> shows an image reconstructed by the simple application of an FFT. <FIG> would be equivalent to the initial image. Image <NUM> shows the results of an FFT after applying a de-ringing filter to the measured gradient echo k-space data. Image <NUM> shows the result of an iteratively calculated corrected image.

In <FIG>, and <FIG> example images from a 3D FFE brain scan acquired at an echo time of <NUM>. (<NUM> Tesla, 1x1x2 mm3 voxel size). <FIG> shows the image reconstructed by simple application of FFT. <FIG> shows the result of FFT after applying a de-ringing filter. <FIG> shows the result of the proposed method. Comparing the left and central image, it is clear that application of the anti-ringing filter increases the size of the signal voids (arrows). The proposed method in <FIG> has smaller signal voids than the FFT image, yet in this reconstruction the same anti-ringing filter as in the reconstruction of the central image was used.

Examples provide for a reconstruction algorithm which may reduce signal voids in gradient echo images and allows applying an anti-ringing filter. Another advantage is that the quantitative accuracy of R2* values, which can be determined from multi-echo GE scans, is improved (see <FIG>, <FIG> below).

<FIG> illustrates an R2* map computed from a standard reconstruction. This is a de-ringing followed by an FFT transform.

<FIG> shows an R2* map calculated according to the first example algorithm disclosed below.

<FIG> shows an image which shows a difference between <FIG> and <FIG> illustrates how the reconstruction method improves the homogeneity of R2* values in regions with strong off-resonance gradients.

In the disclosed algorithms, instead of reconstructing the true object magnetization at echo time TE, the object magnetization is reconstructed without the phase variation that is caused by the off-resonance. To this end, the algorithm uses an off-resonance map df, which may be approximate. The magnetization is determined in an iterative procedure driven by data consistency. Examples may be much faster and easier to use than other algorithms to reduce static off-resonance artifacts.

A first example of a reconstruction algorithm is discussed below.

Let s be the acquired k-space data, df an off-resonance map, and r an anti-ringing filter. The image reconstruction is iteratively improving the image mi:
Let s be the acquired k-space data, df an off-resonance map, and r a de-ringing filter.

The image reconstruction is iteratively improving the image mi:
<IMG>.

Here, upsample is an operation that increases the resolution of an image (a factor of two was used for the result shown in <FIG>). the image containing the off-resonance phase is modeled at a higher spatial resolution than acquired. In this way, the intra voxel dephasing in this space is reduced to an acceptable level.

This iteration scheme converges quickly (<NUM> iterations were used for the result in <FIG>).

The off-resonance map can either be obtained in a separate measurement or, in the case of a multi-echo FFE scan, calculated from the first echoes. The required accuracy of df is fairly low because all phase errors caused by an inaccurate off-resonance map, will be absorbed by the reconstructed magnetization.

The above algorithm may be modified. For example, the initial magnetization image m<NUM> = <NUM>. As an alternative the initial magnetization image may be reconstructed from the acquired k-space data.

An alternative method iteratively calculates a residual which is used to modify the image from the previous iteration. It resembles a compressed sensing algorithm. Below a sample algorithm is detailed using the following conventions: S is a coil sensitivity map, F is a Fourier transform, P: Projection on measured profiles in k-space aka subsampling mask/weights, and Superscript "H" refers to Hermitian conjugate, "-<NUM>" to inverse. Minimization problem <MAT> Here, R is a regularization term, e.g. a smoothness promoting functional Setting the gradient of the objective function with respect to m to zero we get an equation to solve: <MAT> Instead of always upsampling with U and downsampling with UH, we solve the problem in high-resolution, replacing m → mh = Um: <MAT> Initialize m and upsample to mh (step <NUM>)
<IMG>
<IMG>.

The above algorithm may also be combined with parallel imaging. An example algorithm of the above algorithm incorporating parallel imaging is: Minimization problem <MAT> Here, S contains the coil sensitivities, mapping to the measured channels The high-res equation then reads (y is then multi-coil data): <MAT> Initialize m and upsample to mh
<IMG>.

Intra-voxel dephasing in gradient-echo MRI can also lead to signal dropout and other artifacts caused by strong phase-gradients, for example due to strong variations of the off-resonance field. The example below describes a method to correct for these artifacts by exploiting available information in multi-echo gradient echo MRI scans. It leverages model-based reconstruction and builds on the above disclosed method for reducing static B0-induced artifacts. Including multi-echo information, in particular information from shorter echo-times, it is possible to overcome the limitations for correcting errors present in single-echo methods, which is given approximately for a phase-shift of pi/voxel.

The problems of B0-inhomogeneities are well-known in gradient-echo MRI. For example, static B0-off-resonance gradients can lead to intra-voxel dephasing, in particular for low-resolution scans and/or at long echo-times. In addition to the off-resonance gradient, the phase-difference across a voxel is also proportional to the echo-time, so that longer echo-times are more severely affected.

Methods exist to correct for intra-voxel dephasing. However, these can only work up to the limit where the signal is shifted outside the acquired k-space region, which happens approximately when the phase-difference across an acquisition voxel exceeds pi.

For multi-echo gradient scans, for example for R2*-mapping or SWI, additional information is available from short TE echoes. Given a model for the signal behaviour as a function of echo-time, intra-voxel dephasing in late echo-time images can be mitigated.

The algorithm below builds on the above disclosed algorithm and assumes an approximation of the off-resonance field, B', as given. This is not a severe restriction, since the assumed off-resonance map needs only to reflect the strongest gradients. Furthermore, we assume a signal model describing the signal behavior as a function of echo-time, e.g. the mono-exponential <MAT>-decay model given by: <MAT>.

Here, s is the signal at position r, m is the complex magnetization (with only slowly varying phase), <MAT> is the transverse dephasing rate, B' is the assumed approximate off-resonance field (capturing the strong phase variations), ΔB is the remaining off-resonance field not demodulated, which still causes an echo-time dependence, and tj is the echo-time of the j-th echo and γ the gyromagnetic ratio. Symbols with a prime (') are supposed to refer to quantities which include the phase modulation caused by B'. Other models may be appropriate depending on the desired application. Ignoring parallel imaging for simplicity (or compressing multiple channels to one), this can be related the acquired k-space data via the usual Fourier relation, with F the Fourier Transform <MAT> Solving the minimization problem <MAT>.

Yields the parameter maps m and <MAT>. However, due to dephasing, <MAT> will be biased. To compensate, we apply the above disclosed method in the forward model. Instead of directly solving the above minimization problem, instead upsampling to a higher resolution at which the approximate off-resonance field B' is modulated is performed. After Fourier Transform, the signal can be compared with the acquired data (low resolution), to compute a residual.

In detail steps performed in each iteration are the following, given current m, <MAT>, ΔB.

This can work in 2D (given information about B0 gradients across slices) and 3D.

Other signal models that may be applied include: Multi-exponential decay, Multi-Component Models, Water-Fat/Chemical Shift Models, Dictionary Matching, Subspace Projection, and others.

Alternative Algorithms: Instead of projecting on the measured k-space data, a minimization approach could be used similar to Compressed SENSE. In the general case, the B0-demodulation could be fully integrated into CSSense reconstruction.

<FIG> shows the last echo of multi-echo scan with <NUM> echoes after FFT from raw data.

<FIG> shows a corrected image based on the same data at the same echo-time (<NUM>) using the method described in steps <NUM> through <NUM> above. Dephasing is reduced close to the nasal sinus.

In the above equations, the off resonance terms is represented by two terms eiγtjΔB(r) and eiγtjB'(r). However, the above algorithm can easily be modified such that the B' and ΔB terms are replaced with a single term that represents the entire off-resonance field.

Claim 1:
A medical system (<NUM>, <NUM>) comprising:
a memory (<NUM>) storing machine executable instructions (<NUM>);
a processor (<NUM>) configured for controlling the medical system, wherein execution of the machine executable instructions causes the processor to:
receive (<NUM>) measured gradient echo k-space data (<NUM>) from a magnetic resonance imaging system;
receive (<NUM>) an off-resonance phase map (<NUM>) from the magnetic resonance imaging system;
reconstruct (<NUM>) an initial magnetization image (<NUM>) from the measured gradient echo k-space data;
calculate (<NUM>) a modulated image (<NUM>);
calculate (<NUM>) a corrected image (<NUM>) comprising iteratively:
calculating (<NUM>) updated k-space data by applying a data consistency algorithm (<NUM>) to a k-space representation of the modulated image and the measured gradient echo k-space data; and
calculating (<NUM>) an updated image (<NUM>) from the updated k-space data, wherein calculating the updated image comprises applying a smoothing algorithm, wherein the modulated image for further iteration results from the updated image; characterized in that execution of the machine executable instructions further causes the processor to:
calculate (<NUM>) an upsampled phase map (<NUM>) from the off-resonance phase map;
calculate (<NUM>) an upsampled image (<NUM>) from the initial magnetization image, with same chosen resolution of the upsampled image and the upsampled phase map;
wherein calculating the modulated image is performed by modulating the upsampled image with the upsampled phase map;
wherein calculating the updated image further comprises demodulation by the upsampled phase map.