System and method for magnetic resonance imaging with radial sampling of k-space

1. A system for generating an image of a subject using a magnetic resonance imaging (MRI) device, comprising:

at least one storage device including a set of instructions; and

at least one processor configured to communicate with the at least one storage device, wherein when executing the set of instructions, the at least one processor is configured to direct the system to perform operations including:

obtaining a radial sampling scheme including a plurality of radial lines that each pass through a center of k-space, adjacent ones of the plurality of radial lines are spaced by a baseline angular increment;

selecting the plurality of radial lines of the radial sampling scheme, each of the plurality of radial lines is selected in a random and unrepeatable manner, wherein successive selected radial lines are spaced by an integral multiple of the baseline angular increment;

acquiring k-space data along the selected radial lines; and

reconstructing at least one image of the subject based on the acquired k-space data.

2. The system of claim 1 , wherein the selecting the plurality of radial lines of the radial sampling scheme includes:

generating a set of azimuthal angles corresponding to the plurality of radial lines of the radial sampling scheme;

selecting a first radial line corresponding to a first azimuthal angle from the set of azimuthal angles randomly;

selecting a second radial line corresponding to a second azimuthal angle from the set of azimuthal angles excluding the first azimuthal angle randomly;

selecting a k-th radial line corresponding to a k-th azimuthal angle from the set of azimuthal angles excluding previous selected k−1 azimuthal angles,

wherein the k-th azimuthal angle is determined based on at least one random probability derived from intersection angles formed between adjacent ones of previous selected k−1 radial lines; and

wherein 3≤k≤N, k being an integer and N being indicative of the number of the plurality of radial lines of the radial sampling scheme.

3. The system of claim 2 , wherein a sum of the intersection angles is equal to Tr.

4. The system of claim 2 , wherein the selecting a k-th radial line corresponding to a k-th azimuthal angle from the set of azimuthal angles excluding previous selected k−1 azimuthal angles includes:

determining a random probability corresponding to each of the intersection angles formed between adjacent ones of the previous selected k−1 radial lines;

generating a random value;

determining a reference azimuthal angle based on the random value and an intersection angle corresponding to a maximum random probability;

determining, based on the reference azimuthal angle, the k-th azimuthal angle from the set of azimuthal angles excluding previous selected k−1 azimuthal angles; and

selecting the k-th radial line corresponding to the k-th azimuthal angle.

5. The system of claim 4 , wherein the random value is in a range of 0 to 1.

6. The system of claim 2 , wherein the number of the plurality of radial lines of the radial sampling scheme, N, is determined based on a desired image resolution.

7. The system of claim 6 , wherein N is equal to a maximum integer closing to a product of π and a coefficient of the desired image resolution.

8. The system of claim 6 , wherein N is equal to a maximum integer closing to a product of π/2 and a coefficient of the desired image resolution.

9. The system of claim 6 , wherein the baseline angular increment is determined based on the number of the plurality of radial lines of the radial sampling scheme.

10. The system of claim 1 , wherein the acquiring k-space data along the selected radial lines includes:

acquiring the k-space data in accordance with a sequence of the selected radial lines.

11. A method for generating an image of a subject using a magnetic resonance imaging (MRI) device, implemented on a computing device having at least one processor and at least one storage device, comprising:

obtaining a radial sampling scheme including a plurality of radial lines that each pass through a center of k-space, adjacent ones of the plurality of radial lines are spaced by a baseline angular increment;

selecting the plurality of radial lines of the radial sampling scheme, each of the plurality of radial lines is selected in a random and unrepeatable manner, wherein successive selected radial lines are spaced by an integral multiple of the baseline angular increment;

acquiring k-space data along the selected radial lines; and

reconstructing at least one image of the subject based on the acquired k-space data.

12. The method of claim 11 , wherein the selecting the plurality of radial lines of the radial sampling scheme includes:

generating a set of azimuthal angles corresponding to the plurality of radial lines of the radial sampling scheme;

selecting a first radial line corresponding to a first azimuthal angle from the set of azimuthal angles randomly;

selecting a second radial line corresponding to a second azimuthal angle from the set of azimuthal angles excluding the first azimuthal angle randomly;

selecting a k-th radial line corresponding to a k-th azimuthal angle from the set of azimuthal angles excluding previous selected k−1 azimuthal angles,

wherein the k-th azimuthal angle is determined based on at least one random probability derived from intersection angles formed between adjacent ones of previous selected k−1 radial lines; and

wherein 3≤k≤N, k being an integer and N being indicative of the number of the plurality of radial lines of the radial sampling scheme.

13. The method of claim 12 , wherein a sum of the intersection angles is equal to Tr.

14. The method of claim 12 , wherein the selecting a k-th radial line corresponding to a k-th azimuthal angle from the set of azimuthal angles excluding previous selected k−1 azimuthal angles includes:

determining a random probability corresponding to each of the intersection angles formed between adjacent ones of the previous selected k−1 radial lines;

generating a random value;

determining a reference azimuthal angle based on the random value and an intersection angle corresponding to a maximum random probability;

determining, based on the reference azimuthal angle, the k-th azimuthal angle from the set of azimuthal angles excluding previous selected k−1 azimuthal angles; and

selecting the k-th radial line corresponding to the k-th azimuthal angle.

15. The method of claim 14 , wherein the random value is in a range of 0 to 1.

16. The method of claim 12 , wherein the number of the plurality of radial lines of the radial sampling scheme, N, is determined based on a desired image resolution.

17. The method of claim 16 , wherein N is equal to a maximum integer closing to a product of π and a coefficient of the desired image resolution.

18. The method of claim 16 , wherein N is equal to a maximum integer closing to a product of π/2 and a coefficient of the desired image resolution.

19. The method of claim 11 , wherein the acquiring k-space data along the selected radial lines includes:

acquiring the k-space data in accordance with a sequence of the selected radial lines.

20. A non-transitory computer-readable medium, comprising at least one set of instructions, wherein when executed by at least one processor of a computer device, the at least one set of instructions directs the at least one processor to perform operations including:

obtaining a radial sampling scheme including a plurality of radial lines that each pass through a center of k-space, adjacent ones of the plurality of radial lines are spaced by a baseline angular increment;

selecting the plurality of radial lines of the radial sampling scheme, each of the plurality of radial lines is selected in a random and unrepeatable manner, wherein successive selected radial lines are spaced by an integral multiple of the baseline angular increment;

acquiring k-space data along the selected radial lines; and

reconstructing at least one image of a subject based on the acquired k-space data.