Method of autocalibrating parallel imaging interpolation from arbitrary K-space sampling with noise correlations weighted to reduce noise of reconstructed images

1. A Non-transitory computer implemented method of magnetic resonance imaging (MRI) in an MRI system, comprising:

performing a 3D Fourier Transform acquisition with two phase encode directions in the MRI system, wherein phase code locations are chosen so that a total number of phase encodes is less than a Nyquist rate, and closest distances between the phase encode locations, in each of the two phase encode directions, each take on a multiplicity of values;

receiving readout signals through a multi-channel array of a plurality of receivers of the MRI system;

performing an autocalibrating parallel imaging interpolation for each channel of the multi-channel array in order to reconstruct data;

generating a noise correlation between, the reconstructed data of the multi-channel array after performing the autocalibrating parallel imaging interpolation and from the autocalibrating parallel imaging interpolation;

using of the noise correlation in order to suppress noise amplified by the autocalibrating parallel imaging by using the noise correlation in order to weight a data consistency term of a compressed sensing iterative reconstruction;

creating an image from the autocalibration parallel imaging using the noise-weighted data consistency term on the autocalibrating parallel imaging interpolation; and

displaying the image through the MRI system.

2. The Non-transitory computer implemented method, as recited in claim 1 , wherein the autocalibrating parallel imaging interpolation comprises one of GRAPPA or ARC.

3. The Non-transitory computer implemented method, as recited in claim 2 wherein the multiplicity of values is at least 10 different values.

4. The Non-transitory computer implemented method, as recited in claim 3 , wherein the phase encode locations are chosen in a pseudo-random pattern.

5. The Non-transitory computer implemented method, as recited in claim 4 , wherein the pseudo-random pattern is one of a Poisson-disc or a jittered grid sampling pattern with uniform or variable sampling density.

6. The Non-transitory computer implemented method, as recited in claim 4 , wherein performing the autocalibration parallel imaging interpolation provides a noise covariance matrix of the reconstructed data that provides both the confidence level of reconstruction entries and noise correlation.

7. The Non-transitory computer implemented method, as recited in claim 5 , wherein the using of the noise correlation to suppress noise amplified by the autocalibrating parallel imaging comprises applying a de-noising on a slice-by-slice basis using a nonlinear conjugate gradient optimization method.

8. The Non-transitory computer implemented method, as recited in claim 5 , wherein the using of the noise correlation to suppress noise amplified by the autocalibrating parallel imaging comprises using a L1 optimization that uses this noise correlation to correctly form a data consistency constraint.

9. The Non-transitory computer implemented method, as recited in claim 1 , wherein the performing an autocalibrating parallel imaging interpolation and generating a noise correlation uses a GRAPPA interpolation with a 3D kernel.

10. The Non-transitory computer implemented method, as recited in claim 1 , wherein performing the autocalibration parallel imaging interpolation provides a noise covariance matrix of the reconstructed data that provides both the confidence level of reconstruction entries and noise correlation.

11. The Non-transitory computer implemented method, as recited in claim 1 , wherein the phase encode directions are chosen in a pseudo-random pattern.

12. The Non-transitory computer implemented method, as recited in claim 1 , wherein the using of the noise correlation to suppress noise amplified by the autocalibrating parallel imaging comprises applying a de-noising on a slice-by-slice basis using a nonlinear conjugate gradient optimization method.

13. The Non-transitory computer implemented method, as recited in claim 1 , wherein the using of the noise correlation to suppress noise amplified by the autocalibrating parallel imaging comprises using a L1 optimization that uses this noise correlation to correctly form a data consistency constraint.

14. A Non-transitory computer implemented method for providing magnetic resonance imaging (MRI) in an MRI system, comprising:

a) exciting precessing nuclear spins in a region of a subject in the MRI system;

b) simultaneously obtaining a plurality of response signals, representing magnetic resonance signals arising from precessing nuclear spins, from the region respectively with a plurality of RF reception coils of the MRI system, with each response signal representing a pseudo random reduced data set of a totality of all of said response signals;

c) performing an autocalibrating parallel imaging interpolation on the plurality of response signals for each channel of the multi-channel array in order to reconstruct data; and

d) generating a noise correlation between the reconstructed data of the multi-channel array from the autocalibrating parallel imaging interpolation;

e) using the noise correlation in order to suppress noise amplified by the autocalibrating parallel imaging;

f) creating an image from the autocalibration parallel imaging with suppressed noise; and

g) displaying the image through the MRI system.

15. The Non-transitory computer implemented method, as recited in claim 14 , wherein the autocalibrating parallel imaging interpolation comprises one of GRAPPA or ARC.

16. The Non-transitory computer implemented method, as recited in claim 14 , wherein performing the autocalibration parallel imaging interpolation provides a noise covariance matrix of the reconstructed data that provides both the confidence level of reconstruction entries and noise correlation.

17. The Non-transitory computer implemented method, as recited in claim 14 , further comprising applying a compressed-sensing optimization using the noise correlation.

18. Non-transitory The computer implemented method, as recited in claim 14 , wherein the using of the noise correlation in order to suppress noise amplified by the autocalibrating parallel imaging comprises applying a de-noising on a slice-by-slice basis using a nonlinear conjugate gradient optimization method.

19. The Non-transitory computer implemented method, as recited in claim 14 , wherein the using the noise correlation in order to suppress noise amplified by the autocalibrating parallel imaging comprises using a L 1 optimization that uses this noise correlation in order to correctly form a data consistency constraint.

20. The Non-transitory computer implemented method, as recited in claim 14 , wherein the performing an autocalibrating parallel imaging interpolation and generating a noise correlation uses a GRAPPA interpolation with a 3D kernel.