Method and system for accelerated wave data magnetic resonance acquisition

1. A method for generating at least one magnetic resonance (MR) image of an object in an MR system having a plurality of signal receiving coils, the method comprising:

applying a sequence of radio frequency (RF) pulses to generate a plurality of MR signal-echoes;

detecting the plurality of MR signal-echoes with the plurality of signal receiving coils in a 3-dimensional k-space that is undersampled with a plurality of constant radii corkscrew trajectories having different radii resulting in a non-homogeneous undersampled 3-dimensional k-space; and

reconstructing the at least one MR image based on the non-homogeneous undersampled 3-dimensional k-space using a compressed sensing technology.

2. A magnetic resonance (MR) system configured to generate at least one MR image of an object under examination, the MR system comprising:

a radio frequency (RF) controller configured to apply a sequence of RF pulses to generate a plurality of MR signal echoes;

a gradient controller configured to generate magnetic field gradients;

a plurality of signal receiving coils configured to detect MR signal echoes;

an image sequence controller configured to control an application of RF pulses, magnetic field gradients, and detection of MR signal echoes in 3-dimensional k-space such that the 3-dimensional k-space is undersampled with a plurality of constant radii corkscrew trajectories having different radii resulting in a non-homogeneous undersampled 3-dimensional k-space; and

a processor configured to reconstruct the at least one MR image based on the non-homogeneous undersampled 3-dimensional k-space using a compressed sensing technology.

3. The method according to claim 1 , wherein the radii of the plurality of constant radii corkscrew trajectories increase with an increasing distance from a center of the non-homogeneous undersampled 3-dimensional k-space.

4. The method according to claim 1 , wherein the plurality of MR signal-echoes of each of the plurality of constant radii corkscrew trajectories are detected in a first data sampling period that is the same for all of the plurality of constant radii corkscrew trajectories.

5. The method according to claim 4 , wherein a sampling rate with which the plurality of MR signal-echoes are sampled within the first data sampling period is larger for a first constant radii corkscrew trajectory of the plurality of constant radii corkscrew trajectories having a larger radius compared to a sampling rate which with the plurality of MR signal-echoes are sampled within the first sampling period for a second constant radii corkscrew trajectory of the plurality of constant radii corkscrew trajectories having a smaller radius than the first constant radii corkscrew trajectory.

6. The method according to claim 4 , wherein a sampling rate with which the plurality of MR signal-echoes are sampled within the first data sampling period is the same for all of the plurality of constant radii corkscrew trajectories, wherein a number of turns is smaller for a first constant radii corkscrew trajectory of the plurality of constant radii corkscrew trajectories having a larger radius compared to the number of turns for a second constant radii corkscrew trajectory of the plurality of constant radii corkscrew trajectories having a smaller radius than the first constant radii corkscrew trajectory.

7. The method according to claim 1 , wherein the non-homogenous undersampled 3-dimensional k-space is k-space which is incompletely sampled under a Nyquist theorem.

8. A non-transitory computer program product which includes a program and is directly loadable into a memory of the MR system, when executed by a processor of the MR system, causes the processor to perform the method as claimed in claim 1 .

9. A non-transitory computer-readable storage medium with an executable program stored thereon, that when executed, instructs a processor to perform the method of claim 1 .

10. The MR system according to claim 2 , wherein the image sequence controller is configured to sample the non-homogeneous undersampled 3-dimensional k-space such that the radii of the plurality of constant radii corkscrew trajectories increase with an increasing distance from a center of the non-homogeneous undersampled 3-dimensional k-space.

11. The MR system according to claim 2 , wherein the image sequence controller is configured to detect the MR signal-echoes of each of the plurality of constant radii corkscrew trajectories in a first data sampling period which is the same for all of the plurality of constant radii corkscrew trajectories.

12. The MR system according to claim 11 , wherein the image sequence controller is configured to use a sampling rate with which the MR signal-echoes are sampled within the first data sampling period that is larger for a first one of the plurality of constant radii corkscrew trajectories having a larger radius compared to the sampling rate with which the MR signal-echoes are sampled within the first sampling period for a second one of the plurality of constant radii corkscrew trajectories having a smaller radius than the first one of the plurality of constant radii corkscrew trajectories.

13. The MR system according to claim 11 , wherein the image sequence controller is configured to use a sampling rate with which the MR signal-echoes are sampled within the first data sampling period that is the same for all of the plurality of constant radii corkscrew trajectories, wherein a number of turns is smaller for a first constant radii corkscrew trajectory of the plurality of constant radii corkscrew trajectories having a larger radius compared to the number of turns for a second constant radii corkscrew trajectory of the plurality of constant radii corkscrew trajectories having a smaller radius than the first constant radii corkscrew trajectory.