Ruimin Feng, Qing Wu, Jie Feng, Huajun She, Chunlei Liu, Yuyao Zhang, Hongjiang Wei

IEEE TRANSACTIONS ON MEDICAL IMAGING, 43:4, APRIL 2023

Abstract

Parallel imaging is a commonly used technique to accelerate magnetic resonance imaging (MRI) data acquisition. Mathematically, parallel MRI reconstruction can be formulated as an inverse problem relating the sparsely sampled k-space measurements to the desired MRI image. Despite the success of many existing reconstruction algorithms, it remains a challenge to reliably reconstruct a high-quality image from highly reduced k-space measurements. Recently, implicit neural representation has emerged as a powerful paradigm to exploit the internal information and the physics of partially acquired data to generate the desired object. In this study, we introduced IMJENSE, a scan-specific implicit neural representationbased method for improving parallel MRI reconstruction. Specifically, the underlying MRI image and coil sensitivities were modeled as continuous functions of spatial coordinates, parameterized by neural networks and polynomials, respectively. The weights in the networks and coefficients in the polynomials were simultaneously learned directly from sparsely acquired k-space measurements, without fully sampled ground truth data for training. Benefiting from the powerful continuous representation and joint estimation of the MRI image and coil sensitivities, IMJENSE outperforms conventional image or k-space domain reconstruction algorithms. With extremely limited calibration data, IMJENSE is more stable than supervised calibrationless and calibrationbased deep-learning methods. Results show that IMJENSE robustly reconstructs the images acquired at 5× and 6× accelerations with only 4 or 8 calibration lines in 2D Cartesian acquisitions, corresponding to 22.0% and 19.5% undersampling rates. The high-quality results and scanning specificity make the proposed method hold the potential for further accelerating the data acquisition of parallel MRI.

 

Introduction and Methods

MAGNETIC Resonance Imaging (MRI) is a widely used imaging technique in clinical diagnosis and research due to its safety, radiation-free, and excellent soft tissue contrast. However, MRI suffers from the main drawback of long acquisition time. Various strategies have been proposed to accelerate the MRI acquisition by reconstructing artifactfree MRI images from partially sampled k-space data beyond the Nyquist sampling theory. Currently, parallel MRI is used in nearly all clinical systems for scan acceleration. The parallel MRI reconstruction methods exploit the information redundancy of multiple receiver coils in the image domain or the k-space domain. The former requires the explicit precalculation of coil sensitivity maps, while the latter reconstructs the missing k-space data based on learned kernels from a fully sampled auto-calibration signal (ACS) region, the structured low-rankness of multicoil k-space data, or a combination of both. Compressed sensing theory offers an alternative approach to accelerate MRI. The k-space data are nonuniformly undersampled and the resulting incoherent artifacts in images can be mitigated by imposing proper constraints, such as sparsity in the transform domain and low-rankness. These compressed sensing-based methods have shown superior performance in 3D imaging and dynamic imaging. For the 2D Cartesian acquisition, several pseudo-random sampling patterns have been proposed to meet the requirement of incoherent undersampling.

 

Key Results and Conclusions

We have demonstrated a novel deep-learning insight that fundamentally differs from previous deep learning-based parallel MRI reconstruction methods. The proposed IMJENSE is a training database-free method and learns the continuous function representation of the MRI image and coil sensitivities from the partially acquired k-space itself. We tested IMJENSE on different datasets under different conditions. Results show that IMJENSE can improve parallel MRI reconstruction with highly reduced k-space measurements in the 2D Cartesian acquisition. The superior performance and the scan-specific characteristic make the proposed method potential for further speeding up the MRI data acquisition.

 

Fig.1：Overview of the proposed method.

Pixel coordinates are determined by their positions, with 1d1 and 1d2 denoting intervals between adjacent pixels along the x and y directions, d1 and d2 representing the total number of pixels along these directions. These coordinates are stacked into a matrix that serves as input for two MLPs and polynomials, producing vectorized real and imaginary components of an MRI image, along with coil sensitivities. These vectors are then reshaped to create the 2D images and sensitivity maps, which are used for k-space signal prediction. During the training, the MLP weights and the polynomial coefficients are simultaneously optimized by minimizing data consistency loss LDC and total variation loss LTV. When inferring, an additional step is adopted to enforce the data consistency of k-space.

 

Fig. 2：Visualization of hyperparameter search using Bayesian optimization on the FastMRI knee training dataset.

 

Fig.3：Comparisons of different methods on the 15-channel knee dataset with 24 ACS lines at (a-b) R=4 and (c-d) R=5.

The zoomed-in images show that IMJENSE effectively removes noise and artifacts in the magnitude and phase images and exhibits smaller differences relative to the ground truth. The red arrows point to the artifacts in the magnitude images reconstructed by LORAKS and H-DSLR. Quantitative evaluation metrics (PSNR and SSIM) are reported below each image. The 10× error maps are displayed for better visualization.

 

Fig.4：The recvered k-space and the corresponding error map relative to the fully sampled k-space on the knee dataset with 24 ACS lines at (a) R=4 and (b) R=5. The magnitude k-space and errors from the first channel are displayed with a range of [0, 0.01] for better visualization.

 

Fig.5:Comparisons of different methods on the 2-channel macaque brain dataset at R=2 and ACS=100.

(a) and (c) The reconstructed magnitude and phase images. Zoomed-in images show that IMJENSE removes artifacts that are obvious in the reconstructed results of the compared methods. (b) The 5× errors of the reconstructed magnitude images relative to the ground truth. (d) and (f) The magnitude of the recovered k-space and the corresponding errors relative to the fully-sampled k-space data. (e) Undersampling mask.

 

Fig.6: Magnitude and phase coil sensitivity maps from the human brain dataset estimated by (a-b) the ESPIRiT algorithm and (c-d) IMJENSE with ACS=4 and ACS=32, respectively. The coil sensitivity maps from four representative channels are presented.

 

Fig.7: The MRI images reconstructed by (a) IMJENSE-J (i.e., IMJENSE with the pre-estimated coil sensitivity maps by ESPIRiT) and (b) IMJENSE on the human brain dataset at R=5. Red arrows point to the artifacts in the IMJENSE-J results with fewer ACS lines. The PSNR (dB) and SSIM are reported below each image.

 

Fig.8: Comparisons of different methods on the 32-channel human brain dataset with 8 ACS lines at (a) R=5 and (b) R=6. Quantitative evaluation metrics are reported below each image. IMJENSE achieves the highest PSNR and SSIM.

 

Fig.9: The restored k-space and the corresponding errors relative to the fully sampled k-space on the human brain dataset with 8 ACS lines at (a) R=5 and (b) R=6. The magnitude k-space and errors from the first channel are displayed with a range of [0, 0.04] for better visualization.

 

Fig.10: Performance variations of different methods on the human brain dataset as a function of ACS sizes at R=5 and R=6, respectively.

 

Fig.11: Comparisons of different methods on the lesion dataset at R=4 with 8 ACS lines.

The red box indicates the zoomed-in lesion region. Red arrows point to the lesion region that is more noticeable in the reconstruction results of SHLR-SV, H-DSLR, and IMJENSE. Quantitative evaluation metrics are reported below each image. IMJENSE achieves the highest PSNR and SSIM.

 

Fig.12: Comparisons between (b-c) calibration-based supervised MoDL and (d-e) the proposed IMJENSE method at R=4, using 24 and 12 ACS lines, respectively. (a) The ground truth image. Red arrows indicate the severe artifacts in the MoDL results when only 12 ACS lines are used, due to the inaccurate sensitivity maps estimated from a smaller calibration region.

 

Fig.13: (a) One representative knee slice of the reconstructed image.

The region outlined by the red box is displayed with the original size, as well as 2×, 3×, and 4× upsampling obtained by querying the trained MLP using denser coordinate grids. (b) Illustration of the training grid and queried denser grids used in each case.

 

Fig.14: Effects of w0 and λ on the reconstruction results.

 

Fig.15: The convergence of the accelerated framework using hash encoding on the Fast MRI knee dataset at R=5 with 24 ACS lines.

The bottom row shows the training loss at each iteration. The top row shows the reconstruction results and runtime at different iterations. The model takes only 2.48 seconds for the reconstruction of a knee slice with a matrix size of 640 × 368, producing results comparable to the current Framework.

 

 

10.1109/TMI.2023.3342156