Granted Patent B2

US 12,626,438 · App. 17/968,541 · Granted May 12, 2026

Inventors: Ulugbek Kamilov (St. Louis, MO); Hongyu An (St. Louis, MO); Yuyang Hu (St. Louis, MO); Jiaming Liu (St. Louis, MO); Cihat Eldeniz (St. Louis, MO); Weijie Gan (St. Louis, MO); Yasheng Chen (St. Louis, MO)

Assignee: Washington University

G06T11/006G01R33/4818

Abstract

Claims (319)

1 . A computer-aided method of image reconstruction for parallel magnetic resonance (MR) imaging, the method comprising:

a. receiving, using a computing device, a k-space single-coil measurement dataset comprising at least two k-space measurement sets, each k-space measurement set obtained by a single coil of a parallel MR imaging device;

b. transforming, using the computing device, the k-space single-coil measurement dataset to an estimated coil sensitivity map (CSM) using a CSM deep neural network, the transforming comprising:

i. extracting, using the computing device, a small central k-space region from each k-space measurement set;

ii. transforming, using the computing device, each small central k-space region into a single-coil MR image comprising a plurality of complex elements;

iii. separating, using the computing device, a real value and an imaginary value from each complex element of each single-coil MR image and concatenating, using the computing device, the real and imaginary values of all single-coil MR images into a single-coil MR image dataset;

iv. transforming, using the computing device, the single-coil MR image dataset into the estimated CSM using the CSM deep neural network; and

v. calculating, using the computing device, the estimated CSM Ŝ according to the equation:

S

ˆ

=

P

φ

(

p

0

)

;

wherein P φ represents the CSM with predetermined parameters φ and p 0 represents a zero-filled inverse Fourier transform of the small central k-space regions from each k-space measurement set; and

c. transforming, using the computing device, the k-space single-coil measurement dataset and the estimated CSM into a final MR image using an MRI reconstruction module comprising an unfolded regularization by denoising (U-RED) module, the U-RED module comprising a data consistency module and a regularization module, the regularization module comprising a U-RED deep neural network (DNN), wherein:

i. transforming, using the computing device, each k-space measurement set into an intermediate single-coil MR image using a Fourier transform;

ii. performing, using the computing device, an unfolded regularization by denoising comprising K iterations, each iteration comprising:

1. refining the intermediate single-coil MR images using the regularization module by transforming, using the computing device, the intermediate single-coil MR images into an intermediate MR image using the estimated CSM; and transforming, using the computing device, the intermediate MR image into a regularization correction using the U-RED DNN; and

2. enforcing consistency of intermediate single-coil k-space data predicted from the intermediate single-coil MR images with the k-space single-coil measurement dataset by transforming, using the computing device, the intermediate single-coil MR images into intermediate single-coil k-space data using a Fourier transform, transforming, using the computing device, the intermediate single-coil k-space data into predicted intermediate single-coil k-space measurements using an undersampling operator, and calculating, using the computing device, a difference between the predicted intermediate single-coil k-space measurements and the k-space single-coil measurement dataset to produce a data consistency correction; and

3. transforming, using the computing device, the intermediate single-coil MR images as refined after U-RED into the final MR image.

2 . The method of claim 1 , wherein the CSM deep neural network comprises a CSM convolutional neural network.

3 . The method of claim 1 , wherein extracting the small central k-space regions comprises applying, using the computing device, a Hamming window to each k-space measurement set.

4 . The method of claim 1 , wherein transforming each small central k-space region into each corresponding single-coil MR image comprises applying, using the computing device, a zero-filled inverse Fourier transform to each small central k-space region.

5 . The method of claim 1 , wherein each iteration of performing unfolded regularization by denoising further comprises updating, using the computing device, the intermediate single-coil MR images based on the regularization correction and the data consistency correction.

6 . The method of claim 5 , wherein updating the intermediate single-coil MR images based on the regularization correction and the data consistency correction comprises calculating, using the computing device, the updated intermediate single-coil MR images ĉ k+1 according to the equation:

c

ˆ

k

+

1

=

c

ˆ

k

-

γ

k

(

∇

g

(

c

ˆ

k

,

y

)

+

τ

k

⁢

S

ˆ

⁢

R

θ

k

(

S

ˆ

†

⁢

c

ˆ

k

)

)

,

wherein ∇g(ĉ k ,y)=F † ({circumflex over (P)}Fĉ k −y), ĉ k represents the intermediate multi-coil images in the kth iteration of K iterations, γ k (∇g(ĉ k ,y) represents the data consistency correction,

τ

k

⁢

S

ˆ

⁢

R

θ

k

(

S

ˆ

†

⁢

c

ˆ

k

)

)

represents the regularization correction, γ k represents pre-determined consistency parameters, τ k represents pre-determined regularization parameters, Ŝ represents the estimated CSM,

R

θ

k

represents the U-RED DNN with pre-determined parameters θ, Ŝ † represents the inverse of the estimated CSM, F † represents the inverse Fourier transform, {circumflex over (P)} represents the k-space sampling operator, and y represents the k-space single-coil measurement dataset.

7 . The method of claim 6 , further comprising training, using the computing device, the CSM DNN and the U-RED DNN using a stochastic gradient method to jointly optimize parameters φ of the CSM DNN P φ and parameters θ of the U-RED DNN R θ using a training set comprising N multi-coil undersampled k-space measurement pairs

{

y

ˆ

i

,

y

˜

i

}

1

N

,

y

ˆ

i

denoting training measurements, {tilde over (y)} i comprising raw measurements, wherein the measurements in each pair are acquired from the same object.

8 . The method of claim 7 , wherein the multi-coil undersampled measurement pairs

{

y

ˆ

i

,

y

˜

i

}

1

N

are acquired from at least one of: at least two measurement sets of the same object obtained in at least two different parallel MR scans and two subsets of a measurement set obtained in a single parallel MR scan.

9 . The method of claim 7 , wherein the training set does not comprise a ground truth dataset.

10 . The method of claim 7 , wherein training the CSM DNN and the U-RED DNN using a stochastic gradient method further comprises minimizing, using the computing device, a weighted sum loss function given by:

Loss

=

Loss

rec

+

λ

·

Loss

smooth

,

wherein

⁢

Loss

rec

=

1

N

⁢

∑

i

N

ℒ

rec

(

H

~

i

⁢

x

^

i

,

y

~

i

)

+

ℒ

rec

(

H

^

i

⁢

x

~

i

,

y

^

i

)

⁢

and

⁢

Loss

smooth

=

1

N

⁢

∑

i

N



D

⁢

S

^

i



2

2

+



D

⁢

S

~

i



2

2

;

wherein λ is a regularization parameter, L rec denotes the l 2 -norm, and D denotes the discrete gradient.

11 . A system for image reconstruction for parallel magnetic resonance (MR) imaging, the system comprising a computing device comprising at least one processor, the at least one processor configured to:

a. receive a k-space single-coil measurement dataset comprising at least two k-space measurement sets, each k-space measurement set obtained by a single coil of a parallel MR imaging device;

b. transform the k-space single-coil measurement dataset to an estimated coil sensitivity map (CSM) using a CSM deep neural network comprising a CSM convolutional neural network by:

i. extracting a small central k-space region from each k-space measurement set;

ii. transforming each small central k-space region into a single-coil MR image comprising a plurality of complex elements;

iii. separating a real value and an imaginary value from each complex element of each single-coil MR image and concatenating the real and imaginary values of all single-coil MR images into a single-coil MR image dataset;

iv. transforming the single-coil MR image dataset into the estimated CSM using the CSM deep neural network;

v. calculating the estimated CSM Ŝ according to the equation:

S

ˆ

=

P

φ

(

p

0

)

;

wherein P φ represents the CSM with predetermined parameters φ and p 0 represents a zero-filled inverse Fourier transform of the small central k-space regions from each k-space measurement set; and

c. transform the k-space single-coil measurement dataset and the estimated CSM into a final MR image using an MRI reconstruction module by:

i. transforming each k-space measurement set into an intermediate single-coil MR image using a Fourier transform;

ii. performing an unfolded regularization by denoising comprising K iterations, each iteration comprising:

1. refining the intermediate single-coil MR images using the regularization module by;

a. transforming the intermediate single-coil MR images into an intermediate MR image using the estimated CSM; and

b. transforming the intermediate MR image into a regularization correction using the U-RED DNN; and

2. enforcing consistency of intermediate single-coil k-space data predicted from the intermediate single-coil MR images with the k-space single-coil measurement dataset by:

a. transforming the intermediate single-coil MR images into intermediate single-coil k-space data using a Fourier transform:

b. transforming the intermediate single-coil k-space data into predicted intermediate single-coil k-space measurements using an undersampling operator; and

c. calculating a difference between the predicted intermediate single-coil k-space measurements and the k-space single-coil measurement dataset to produce a data consistency correction, and

iii. transforming the intermediate MR image as refined after U-RED into the final MR image.

12 . The system of claim 11 , wherein the at least one processor is further configured to enforce consistency of the intermediate single-coil k-space data by:

a. transforming the intermediate single-coil MR images into intermediate single-coil k-space data using a Fourier transform;

b. transforming the intermediate single-coil k-space data into predicted intermediate single-coil k-space measurements using an undersampling operator; and

c. calculating a difference between the predicted intermediate single-coil k-space measurements and the k-space single-coil measurement dataset to produce a data consistency correction.

13 . The system of claim 12 , wherein the at least one processor is further configured to performing unfolded regularization by denoising iteratively by updating the intermediate single-coil MR images based on the regularization correction and the data consistency correction.

14 . The system of claim 13 , wherein the at least one processor is further configured to update the intermediate single-coil MR images based on the regularization correction and the data consistency correction by calculating, the updated intermediate single-coil MR images ĉ k+1 according to the equation:

c

ˆ

k

+

1

=

c

ˆ

k

-

γ

k

(

∇

g

(

c

ˆ

k

,

y

)

+

τ

k

⁢

S

ˆ

⁢

R

θ

k

(

S

ˆ

†

⁢

c

ˆ

k

)

)

,

wherein ∇g(ĉ k ,y)=F † ({circumflex over (P)}Fĉ k −y), ĉ k represents the intermediate multi-coil images in the kth iteration of K iterations, γ k (∇g(ĉ k ,y) represents the data consistency correction,

τ

k

⁢

S

ˆ

⁢

R

θ

k

(

S

ˆ

†

⁢

c

ˆ

k

)

)

represents the regularization correction, γ k represents pre-determined consistency parameters, τ k represents pre-determined regularization parameters, Ŝ represents the estimated CSM,

R

θ

k

represents the U-RED DNN with pre-determined parameters θ, Ŝ † represents the inverse of the estimated CSM, F † represents the inverse Fourier transform, {circumflex over (P)} represents the k-space sampling operator, and y represents the k-space single-coil measurement dataset.

Assignments (1)

Continuity (2)

References Cited (16)