System and method for random cartesian acquisition with projection reconstruction-like sampling

1. A method for producing a magnetic resonance image of a subject with a magnetic resonance imaging (MRI) system, the method comprising the steps of:

a) acquiring k-space image data from a subject arranged in an MRI system by performing a pulse sequence comprising the steps of:

i) determining a k-space sampling pattern that divides k-space into a central region and periphery of k-space surrounding the central region;

ii) dividing the periphery of k-space into a plurality of radially-extending sectors extending along a radial direction away from the central region, wherein the plurality of radially-extending sectors include a width transverse to the radial direction that is defined by a vane angle chosen to be a sufficiently small value to cause a point spread function (PSF) to have a primary two-dimensional cross-correlation 10- to 1000-fold larger than the primary side-lobe;

iii) acquiring imaging data from at least the radially-extending sectors to undersample the periphery of k-space by only sampling k-space within the plurality of radial sectors;

b) reconstructing an image of the subject using the imaging data.

2. The method of claim 1 wherein the vane angle has a value of less than 1 degree.

3. The method of claim 1 wherein the vane angle has a value of less than 0.001 degrees.

4. The method of claim 1 wherein the vane angle has a value of 0.000000001 degrees.

5. The method of claim 1 wherein the radially-extending sectors are arranged asymmetrical about the central region.

6. The method of claim 1 wherein step iii) includes sampling k-space locations within the central region and each of the radially-extending sectors over a plurality of repetitions.

7. The method of claim 6 wherein step iii) includes sampling k-space locations within the central region more frequently than the radially-extending sectors.

8. The method of claim 1 wherein step iii) includes sampling k-space locations within the central region of k-space using an elliptical centric sampling order.

9. The method of claim 1 wherein step iii) includes sampling k-space locations within the radially-extending sectors of k-space using an elliptical centric sampling order.

10. The method of claim 1 wherein step iii) includes sampling all k-space locations in a first predetermined subset of the radially-extending sectors before sampling k-space locations in a second predetermined subset of the radially-extending sectors.

11. The method of claim 10 wherein the first subset of the radially-extending sectors and the second subset of radially-extending sectors are arranged in an alternating fashion radially about the central region of k-space.

12. A magnetic resonance imaging (MRI) system, the system comprising:

a magnet system configured to generate a polarizing magnetic field about at least a portion of a subject arranged in the MRI system;

a plurality of gradient coils configured to apply a gradient field to the polarizing magnetic field;

a radio frequency (RF) system configured to apply an RF excitation field to a region of interest (ROI) in the subject and acquire MR image data from the ROI;

a computer system programmed to:

control the plurality of gradient coils and the RF system to:

perform a pulse sequence comprising the steps of:

i) determine a k-space sampling pattern that divides k-space into a central region and periphery of k-space surrounding the central region;

ii) divide the periphery of k-space into a plurality of radially-extending sectors defined by trigonometric functions to extend along a radial direction away from the central region, wherein the plurality of radially-extending sectors include a width transverse to the radial direction that is defined by a vane angle chosen to be greater than a floating point precision of the trigonometric functions that define the radially-extending sectors;

iii) acquire imaging data from at least the radially-extending sectors to undersample the periphery of k-space by only sampling k-space within the plurality of radial sectors; and

reconstruct an image of the subject using the imaging data.

13. The system of claim 12 wherein the vane angle has a value of less than 1 degree.

14. The system of claim 12 wherein the vane angle has a value of 0.000000001 degrees.

15. The system of claim 12 wherein the radially-extending sectors are arranged asymmetrical about the central region.

16. The system of claim 12 wherein step iii) includes sampling k-space locations within the central region and each of the radially-extending sectors over a plurality of repetitions.

17. The system of claim 16 wherein step iii) includes sampling k-space locations within the central region more frequently than the radially-extending sectors.

18. The system of claim 12 wherein step iii) includes sampling k-space locations within the central region of k-space using an elliptical centric sampling order.

19. The system of claim 12 wherein step iii) includes sampling k-space locations within the radially-extending sectors of k-space using an elliptical centric sampling order.

20. A method for producing a magnetic resonance image of a subject with a magnetic resonance imaging (MRI) system, the method comprising the steps of:

a) acquiring k-space image data from a subject arranged in an MRI system by performing a pulse sequence comprising the steps of:

i) dividing k-space into a plurality of radially-extending sectors extending along a radial direction away from an origin of k-space, wherein the plurality of radially-extending sectors include a width transverse to the radial direction that is defined by a vane angle chosen to be great than a floating point precision of the trigonometric functions that define the radially-extending sectors;

ii) acquiring imaging data from at least the radially-extending sectors to undersample the periphery of k-space by only sampling k-space within the plurality of radial sectors;

b) reconstructing an image of the subject using the imaging data.