Systems and Methods for Efficiently Generating Magnetic Resonance Images from Incomplete Data

• US 20150309136A1
• Filed: 04/23/2015
• Published: 10/29/2015
• Est. Priority Date: 04/25/2014
• Status: Active Grant

• Current Assignee: Mayo Foundation For Medical Education And Research (Mayo Clinic)
• Original Assignee: Mayo Foundation For Medical Education And Research (Mayo Clinic)
• Inventors: Shu, Yunhong, Manduca, Armando, Trzasko, Joshua D., Bernstein, Matthew A.
• Granted Patent: US 10,048,338 B2
• Time in Patent Office: Days
• US Class Current: 1/1
• CPC Class Codes: G01R 33/4826 in three dimensions
• CPC Class Codes: G01R 33/5611 Parallel magnetic resonance imaging, e.g. sensitivity encoding [SENSE], simultaneous acquisition of spatial harmonics [SMASH], unaliasing by Fourier encoding of the overlaps using the temporal dimension [UNFOLD], k-t-broad-use linear acquisition speed-up technique [k-t-BLAST], k-t-SENSE structural details of arrays of sub-coils G01R33/3415

Abstract

Systems and methods for efficiently generating MR images are provided. The method comprises acquiring k-space MR data, reconstructing an MR image from the k-space MR data, and generating the MR image. The MR image is reconstructed using an alternative-direction-method-of-multiplier (ADMM) strategy that decomposes an optimization problem into subproblems, and at least one of the subproblems is further decomposed into small problems. The further decomposition is based on Woodbury matrix identity and uses a diagonal preconditioner based on non-Toeplitz models.

Claims

1. A method for generating a magnetic resonance (MR) image, the method comprising:

a) acquiring k-space MR data;

b) reconstructing an MR image from the k-space MR data by;

i) using an alternative-direction-method-of-multiplier (ADMM) strategy that decomposes an optimization problem into subproblems; and

ii) decomposing at least one of the subproblems based on a Woodbury matrix identity and using a diagonal preconditioner (PC) based on non-Toeplitz models.

2. The method of claim 1, wherein the k-space MR data is acquired with a non-Cartesian scanning trajectory.

3. The method of claim 1, wherein the diagonal PC is of form P=(D⁻

1+μ

I)<sup>−

1</sup>, where D≈

(AA*)<sup>−

1</sup>, A is a Fourier-based sampling operator that includes off-resonance effects, I is an identify matrix, and μ

is a user-selected parameter.

4. A magnetic resonance imaging (MRI) 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 magnetic gradient system including a plurality of magnetic gradient coils configured to apply at least one magnetic gradient field to the polarizing magnetic field;

a radio frequency (RF) system configured to apply an RF field to the subject and to receive magnetic resonance (MR) signals therefrom;

a computer system programmed to;

a) control the gradient system and the RF system to acquire k-space MR data;

b) reconstruct an MR image from the k-space MR data using an alternative-direction-method-of-multiplier (ADMM) strategy that decomposes an optimization problem into subproblems, wherein at least one of the subproblems is further decomposed based on Woodbury matrix identity and using a diagonal preconditioner (PC) based on non-Toeplitz models; and

c) generate the MR image.

5. The system of claim 4, wherein the k-space MR data is acquired with a non-Cartesian scanning trajectory.

6. The system of claim 4, wherein the diagonal PC is of form P=(D⁻

1+μ

I)<sup>−

1</sup>, where D≈

(AA*)<sup>−

1</sup>, A is a Fourier-based sampling operator that includes off-resonance effects, I is an identify matrix, and μ

is a user-selected parameter.

7. A method for generating a magnetic resonance (MR) image, the method comprising:

a) acquiring k-space MR data;

b) reconstructing an MR image from the k-space MR data using an alternative-direction-method-of-multiplier (ADMM) strategy that decomposes an optimization problem into subproblems, wherein at least one of the subproblems is further decomposed based on Woodbury matrix identity and using a diagonal preconditioner (PC) based on non-Toeplitz models; and

c) generating the MR image.

8. The method of claim 7, wherein the k-space MR data is acquired with a non-Cartesian scanning trajectory.

9. The method of claim 7, wherein the diagonal PC is of form P=(D⁻

1+μ

I)<sup>−

1</sup>, where D≈

(AA*)<sup>−

1</sup>, A is a Fourier-based sampling operator that includes off-resonance effects, I is an identify matrix, and μ

is a user-selected parameter.