Systems and methods for efficiently generating magnetic resonance images from incomplete data

• US 10,048,338 B2
• Filed: 04/23/2015
• Issued: 08/14/2018
• 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.
• Primary Examiner(s): Koval, Melissa
• Assistant Examiner(s): Fetzner, Tiffany
• Application Number:
  US14/694,621
• Publication Number:
  US 20150309136A1
• Time in Patent Office: 1,209 Days
• Field of Search: 324300-322, 324202, 600407-435, 382128-131
• 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 of using a preconditioned optimization strategy in generating a magnetic resonance (MR) image with an accelerated compressed sensing reconstruction, the method comprising:

a) acquiring k-space MR data with a magnetic resonance imaging system;

b) reconstructing an MR image from the acquired k-space, with an accelerated compressed sensing reconstruction process that utilizes a computer processor in communication with the magnetic resonance imaging system by;

i) implementing the use of an alternative-direction-method-of-multiplier (ADMM) strategy in the reconstruction of the generated MR image that initially decomposes the optimization of the ADMM strategy into sub problems before reconstructing the MR image with the computer processor in communication with the magnetic resonance imaging system;

ii) after completing step i), further decomposing at least one of the subproblems of step i) by the use of a Woodbury matrix identity having a diagonal preconditioner (PC) that is based on non-Toeplitz matrix models and

iii) after completing step ii), solving each of the decomposed sub problems with the computer processor in communication with the magnetic resonance imaging system,

whereby the accelerated compressed sensing reconstruction process of steps i), ii) and iii) are utilized in order to generate, provide on a display, and/or store in a memory, the magnetic resonance image resulting from performing this Woodbury preconditioned ADMM optimization strategy.

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

3. The method of claim 1, wherein the diagonal PC has a mathematically written form of 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 around 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 onto the polarizing magnetic field;

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

a computer system programmed to;

a) control the gradient system and the RF system in order to acquire k-space MR data with the magnetic resonance imaging system;

b) reconstruct an MR image from the acquired k-space MR data with the computer processor of the magnetic resonance imaging system by;

i) implementing the use of an alternative-direction-method-of-multiplier (ADMM) strategy in the reconstruction of the generated MR image that initially decomposes the optimization problem, of the ADMM strategy into subproblems, before reconstructing the MR image with the computer processor of the magnetic resonance imaging system;

ii) wherein at least one of the subproblems of step i) is further decomposed after completing step i) by the use of a Woodbury matrix identity having a diagonal preconditioner (PC) that is based on non-Toeplitz matrix models and

iii) after completing step ii), solving each of the decomposed sub problems with the computer processor, of the magnetic resonance imaging system,

whereby steps i), ii) and iii) are utilized in order to generate, provide on a display, and/or store in a memory, the MR image resulting from performing this preconditioned Woodbury ADMM optimization strategy, as an output of the magnetic resonance imaging system.

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

6. The MRI system of claim 4, wherein the diagonal PC has a mathematically written form of 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 of using an alternative-direction-method-of-multiplier (ADMM) strategy that decomposes the optimization into subproblems based on a Woodbury matrix identity using a diagonally preconditioned non-Toeplitz matrix model when generating a magnetic resonance (MR) image, with a magnetic resonance imaging system the method comprising:

a) acquiring k-space MR data with the magnetic resonance imaging system;

b) reconstructing an MR image from the acquired k-space MR data with the computer processor in communication with the magnetic resonance imaging system by;

i) implementing the use of an alternative-direction-method-of-multiplier (ADMM) strategy in the reconstruction of the generated MR image that initially decomposes the optimization problem, of the ADMM strategy into subproblems, before reconstructing the MR image with the computer processor of the magnetic resonance imaging system;

ii) wherein at least one of the subproblems of step i) is further decomposed after completing step i) by the use of a Woodbury matrix identity having a diagonal preconditioner (PC) that is based on non-Toeplitz matrix models; and

iii) after completing step ii), solving each of the decomposed subproblems with the computer processor of the magnetic resonance imaging system, in order to generate, provide on a display, and/or store in a memory, the MR image resulting from performing this method using the magnetic resonance imaging system and the computer processor in communication with the magnetic resonance imaging system.

8. The MRI method of claim 7, wherein the k-space MR data is acquired, by the magnetic resonance imaging system, with a non-Cartesian scanning trajectory.

9. The MRI method of claim 7, wherein the diagonal PC has a mathematically written form of 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.