Method and magnetic resonance apparatus for acquisition of MR data of a two-dimensional volume segment

1. A method for acquiring magnetic resonance (MR) data relating to a pre-determined two-dimensional volume segment within an examination object, comprising:

in a computer, for an MR data acquisition sequence in which MR signals acquired from the examination object are entered as numerical values into an electronic memory organized as k-space so as to thereby sample k-space, making a randomized determination of respective points to be sampled with said numerical values in k-space, that will cause k-space to be undersampled because only the determined points in k-space to-be-sampled are then sampled;

with said computer, operating a magnetic resonance data acquisition scanner so as to execute said data acquisition sequence, while the examination object is situated therein, in order to acquire said MR signals from the pre-determined two-dimensional volume segment within the examination object for the randomized determined points to be sampled, and entering said numerical values of said MR signals into said electronic memory organized as k-space at said randomized determined points, thereby resulting in said electronic memory comprising an undersampled set of k-space data;

in said computer executing a reconstruction algorithm in order to generate image data from said undersampled set of k-space data that form an image of said two-dimensional volume segment that, due to said randomized determination of points sampled in k-space, has a same image content as an image reconstructed from a fully sampled set of k-space data for said two-dimensional volume segment; and

displaying said image of said two-dimensional volume segment, with said image content, reconstructed from said undersampled set of k-space data, at a display screen.

2. A method as claimed in claim 1 comprising, in said computer:

defining each of said points to be sampled in polar coordinates defined by an angle on an axis proceeding through a center of k-space and a distance from said center; and

using, as said randomized determination of said points to be sampled, a randomized determination based on a constant density of said points to be sampled as a function of said angle and a density of said points to be sampled that decreases with increasing distance from said center.

3. A method as claimed in claim 2 comprising, in said randomized determination of said points to be sampled, using radial or spiral trajectories in k-space that began at a center of k-space, and determining said points to be sampled with respect to said trajectories.

4. A method as claimed in claim 3 comprising:

in said computer, in said randomized determination of said points to be sampled, determining intermediate points on said trajectories, with each intermediate point in polar coordinates being defined by an angle with respect to said axis through said center of k-space, and a distance from said center; and

determining each point to be sampled starting from one of said intermediate points, with an angle of the respective intermediate point being assigned a random value.

5. A method as claimed in claim 1 comprising allowing a single point in k-space to be determined multiple times as a point to be sampled in said randomized determination.

6. A method as claimed in claim 1 comprising allowing a single point in k-space to be determined only once as a point to be sampled in said randomized determination.

7. A method as claimed in claim 1 comprising, in said computer:

determining a sequence in which said points to be sampled are sampled, with a distance between two of said points to be sampled that are adjacent to each other in said sequence being as small as possible.

8. A method as claimed in claim 1 comprising acquiring said MR data by operating said MR apparatus with a plurality of receiving antennas in a parallel acquisition technique.

9. A method as claimed in claim 1 comprising, in said computer:

moving each determined point to be sampled to a grid point on a pre-determined grid in k-space;

defining said grid in k-space by parallel first straight lines and parallel second straight lines, said first straight line being perpendicular to said second straight lines;

each two adjacent lines among said first straight lines having a distance therebetween and each two adjacent lines among said second straight lines also having said distance therebetween; and

each grid point in said pre-determined grid in k-space corresponding to a point of interception of one of said first straight lines with one of said second straight lines.

10. A method for acquiring magnetic resonance (MR) data relating to a pre-determined two-dimensional volume segment within an examination object, comprising:

in a computer, for an MR data acquisition sequence in which MR signals acquired from the examination object are entered as numerical values into an electronic memory organized as k-space so as to thereby sample k-space, making a determination of respective points to be sampled with said numerical values in k-space using radial or spiral trajectories in k-space that begin at a center of k-space, that will cause k-space to be undersampled because only the determined points in k-space are then sampled;

in said computer, defining gradient fields to be activated in said MR data acquisition sequence so as to move each determined point to be sampled to a grid point on a pre-determined grid in k-space;

in said computer, defining said gradient field so as to produce said grid in k-space by parallel first straight lines and parallel second straight lines, said first straight line being perpendicular to said second straight lines with each two adjacent lines among said first straight lines having a distance therebetween and each two adjacent lines among said second straight lines also having said distance therebetween, and with each grid point in said pre-determined grid in k-space corresponding to a point of interception of one of said first straight lines with one of said second straight lines;

from said computer, operating a magnetic resonance data acquisition scanner so as to execute said data acquisition sequence, while the examination object is situated therein, in order to acquire said MR signals from the pre-determined two-dimensional volume segment within the examination object for the randomized determined points to be sampled, and entering said numerical values of said MR signals into said electronic memory organized as k-space at said randomized determined points, thereby resulting in said electronic memory comprising an undersampled set of k-space data;

in said computer, executing a reconstruction algorithm in order to generate image data from said undersampled set of k-space data that form an image of said two-dimensional volume segment that, due to said randomized determination of points sampled in k-space, has a same image content as an image reconstructed from a fully sampled set of k-space data for said two-dimensional volume segment; and

displaying said image of said two-dimensional volume segment, with said image content, reconstructed from said undersampled set of k-space data, at a display screen.

11. A magnetic resonance apparatus comprising:

a magnetic resonance scanner;

an electronic memory organized as k-space;

a computer configured, for an MR data acquisition sequence in which MR signals acquired from the examination object are entered as numerical values into said electronic memory organized as k-space so as to thereby sample k-space, to make a randomized determination of respective points to be sampled in k-space, that will cause k-space to be undersampled because only the determined points in k-space are then sampled;

said computer being configured to operate the magnetic resonance scanner so as to execute said data acquisition sequence, while an examination object is situated therein, in order to acquire said MR signals from the pre-determined two-dimensional volume segment within the examination object for the randomized determined points to be sampled, and to enter said numerical values of said MR signals into the electronic memory organized as k-space at said randomized determined points, thereby resulting in said electronic memory comprising an undersampled set of k-space data;

said computer being configured to execute a reconstruction algorithm in order to generate image data from said undersampled set of k-space data that form an image of said two-dimensional volume segment that, due to said randomized determination of points sampled in k-space, has a same image content as an image reconstructed from a fully sampled set of k-space data for said two-dimensional volume segment; and

said computer being configured to display said image of said two-dimensional volume segment, with said image content, reconstructed from said undersampled set of k-space data, at a display screen.

12. A magnetic resonance apparatus comprising:

a magnetic resonance scanner;

an electronic memory organized as k-space;

a computer configured, for an MR data acquisition sequence in which MR signals acquired from the examination object are entered as numerical values into an electronic memory organized as k-space so as to thereby sample k-space, to make a determination of respective points to be sampled with said numerical values in k-space using radial or spiral trajectories in k-space that begin at a center of k-space, that will cause k-space to be undersampled because only the determined points in k-space are then sampled;

said computer being configured to define gradient fields to be activated in said MR data acquisition sequence so as to move each determined point to be sampled to a grid point on a pre-determined grid in k-space;

said computer being configured to define said gradient fields so as to produce said grid in k-space by parallel first straight lines and parallel second straight lines, said first straight line being perpendicular to said second straight lines, with each two adjacent lines among said first straight lines having a distance therebetween and each two adjacent lines among said second straight lines also having said distance therebetween and with each grid point in said pre-determined grid in k-space corresponding to a point of interception of one of said first straight lines with one of said second straight lines;

said computer being configured to operate the magnetic resonance scanner so as to execute said data acquisition sequence, while an examination object is situated therein, so as to acquire said MR signals from the pre-determined two-dimensional volume segment within the examination object for the randomized determined points to be sampled, and to enter said numerical values of said MR signals into the electronic memory organized as k-space at said randomized determined points, thereby resulting in said electronic memory comprising an undersampled set of k-space data;

said computer being configured to execute a reconstruction algorithm in order to generate image data from said undersampled set of k-space data that form an image of said two-dimensional volume segment that, due to said randomized determination of points sampled in k-space, has a same image content as an image reconstructed from a fully sampled set of k-space data for said two-dimensional volume segment; and

said computer being configured to display said image of said two-dimensional volume segment, with said image content, reconstructed from said undersampled set of k-space data, at a display screen.

13. 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 apparatus, said programming instructions causing said computer system to:

make for an MR data acquisition sequence in which MR signals acquired from the examination object are entered as numerical values into an electronic memory organized as k-space so as to thereby sample k-space, a randomized determination of respective points to be sampled with said numerical values in k-space, that will cause k-space to be undersampled because only the determined points in k-space are then sampled;

operate a magnetic resonance data acquisition scanner so as to execute said data acquisition sequence, while the examination object is situated therein, to acquire said MR signals from the pre-determined two-dimensional volume segment within the examination object for the randomized determined points to be sampled, and enter said numerical value of said MR signals into said electronic memory organized as k-space at said determined points, thereby resulting in said electronic memory comprising an undersampled set of k-space data;

execute a reconstruction algorithm in order to generate image data from said undersampled set of k-space data that form an image of said two-dimensional volume segment that, due to said randomized determination of points sampled in k-space, has a same image content as an image reconstructed from a fully sampled set of k-space data for said two-dimensional volume segment; and

display said image of said two-dimensional volume segment, with said image content, reconstructed from said undersampled set of k-space data, at a display screen.

14. 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 apparatus having a magnetic resonance data acquisition scanner, said programming instructions causing said computer system to:

make, for an MR data acquisition sequence in which MR signals acquired from the examination object are entered as numerical values into an electronic memory organized as k-space so as to thereby sample k-space, a determination of respective points to be sampled with said numerical values in k-space using radial or spiral trajectories in k-space that begin at a center of k-space, that will cause k-space to be undersampled because only the determined points in k-space are then sampled;

define gradient fields to be activated in said MR data acquisition sequence so as to move each determined point to be sampled to a grid point on a pre-determined grid in k-space, with said grid defined in k-space by parallel first straight lines and parallel second straight lines said first straight line being perpendicular to said second straight lines with each two adjacent lines among said first straight lines having a distance therebetween and each two adjacent lines among said second straight lines also having said distance therebetween, and with each grid point in said pre-determined grid in k-space corresponding to a point of interception of one of said first straight lines with one of said second straight lines;

operate the magnetic resonance data acquisition scanner so as to execute said data acquisition sequence, while the examination object is situated therein, in order to acquire said MR signals from the pre-determined two-dimensional volume segment within the examination object for the randomized determined points to be sampled, and enter said numerical values of said MR signals into said electronic memory organized as k-space at said randomized determined points, thereby resulting in said electronic memory comprising an undersampled set of k-space data;

in said computer, execute a reconstruction algorithm in order to generate image data from said undersampled set of k-space data that form an image of said two-dimensional volume segment that, due to said randomized determination of points sampled in k-space, has a same image content as an image reconstructed from a fully sampled set of k-space data for said two-dimensional volume segment; and

said computer being configured to display said image of said two-dimensional volume segment, with said image content reconstructed from said undersampled set of k-space data, at a display screen.