Search

US-12626438-B2 - Self-supervised joint image reconstruction and coil sensitivity calibration in parallel MRI without ground truth

US12626438B2US 12626438 B2US12626438 B2US 12626438B2US-12626438-B2

Abstract

Systems and methods for image reconstruction for parallel MR imaging are disclosed that receive a k-space single-coil measurement dataset that includes at least two k-space single-coil measurement sets, transforming the k-space single-coil measurement dataset to an estimated CSM using a coil sensitivity estimation module, and transforming the k-space single-coil measurement dataset and the estimated CSM into a final MR image using an MRI reconstruction module. In some aspects, the coil sensitivity estimation module and MRI reconstruction module include deep learning neural networks trained without the use of ground truth data.

Inventors

  • Ulugbek Kamilov
  • Hongyu An
  • Yuyang Hu
  • Jiaming LIU
  • Cihat Eldeniz
  • Weijie Gan
  • Yasheng Chen

Assignees

  • WASHINGTON UNIVERSITY

Dates

Publication Date
20260512
Application Date
20221018

Claims (14)

  1. 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. 2 . The method of claim 1 , wherein the CSM deep neural network comprises a CSM convolutional neural network.
  3. 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. 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. 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. 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. 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. 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. 9 . The method of claim 7 , wherein the training set does not comprise a ground truth dataset.
  10. 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. 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. 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. 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. 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.

Description

CROSS-REFERENCE TO RELATED APPLICATIONS This application claims priority from U.S. Provisional Application Ser. No. 63/256,962 filed on Oct. 18, 2021, which is incorporated herein by reference in its entirety. STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT Not applicable. MATERIAL INCORPORATED-BY-REFERENCE Not applicable. FIELD OF THE INVENTION The present disclosure generally relates to systems and methods of performing parallel MR imaging (PMRI). BACKGROUND OF THE INVENTION Magnetic resonance imaging (MRI) is one of the leading diagnostic modalities in radiology. It is well-known that data acquisition in MRI is relatively slow compared to other popular diagnostic modalities such as computed tomography (CT). As a consequence, there has been broad interest in techniques for improving the speed of MRI data acquisition. Parallel MRI (PMRI) is one of the most widely used acceleration strategies that relies on the spatial encoding provided by multiple receiver coils to reduce the amount of data that is acquired. In order to combine the data collected by multiple coils, PMRI requires the calibration of coil sensitivities. Calibration can be performed either in k-space or in the image space using coil sensitivity maps (CSMs). Compressed sensing (CS) MRI is a complementary technique that is used for further accelerating data collection by exploiting prior knowledge (sparsity, low-rankness) on the unknown image. Over the past few years, deep learning (DL) has gained popularity for image reconstruction in CS-MRI due to its excellent performance. Recent work has shown the potential of jointly estimating high-quality images and CSMs in an end-to-end manner. However, these methods require fully sampled ground-truth data for the supervised training of the corresponding deep neural networks, making their application challenging when ground truth is unavailable. On the other hand, there has also been broad interest in developing self-supervised DL methods that rely exclusively on the information available in the undersampled measurements. The self-supervised DL in the context of joint image reconstruction and coil sensitivity estimation may be a potential advancement in CS-MRI. SUMMARY OF THE INVENTION Among the various aspects of the present disclosure is the provision of systems and methods for reconstructing parallel MR images from at least two single-coil k-space measurement sets without any need for CSM calibration using deep learning models trained without any need for ground truth data. In one aspect, a computer-aided method of image reconstruction for parallel MR imaging is disclosed that includes receiving 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; transforming, using the computing device, the k-space single-coil measurement dataset to an estimated CSM using a coil sensitivity estimation module; and 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. In some aspects, the coil sensitivity estimation module comprises a CSM deep neural network. In some aspects, the deep neural network comprises a CSM convolutional neural network. In some aspects, transforming the k-space single-coil measurement dataset to an estimated CSM further comprises: extracting a small central k-space region from each k-space measurement set; transforming each small central k-space region into a single-coil MR image comprising a plurality of complex elements, and transforming the single-coil MR images into the estimated CSM using the CSM deep neural network. In some aspects, extracting the small central k-space regions comprises applying a Hamming window to each k-space measurement set. In some aspects, transforming each small central k-space region into a corresponding single-coil MR image comprises applying a zero-filled inverse Fourier transform to each small central k-space region. In some aspects, transforming the k-space single-coil measurement dataset to an estimated CSM further comprises: 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, and transforming the single-coil MR image dataset into the estimated CSM using the CSM deep neural network. In some aspects, the method further comprises transforming the single-coil MR image dataset into the estimated CSM using the CSM deep neural network further comprises calculating the estimated CSM Ŝ according to the equation: Ŝ=Pφ(p0) wherein Pφ represents the CSM with predetermined parameters φ and p0 represents the zero-filled inverse Fourier transform of the small central k-space regions from each k-space measurement set. In some aspects, the MRI reconstruction modul