Simultaneous CT-MRI Reconstruction for Constrained Imaging Geometries Using Structural Coupling and Compressive Sensing

Abstract

Objective: A unified reconstruction framework is presented for simultaneous CT-MRI reconstruction.

Methods: In an ideal CT-MRI scanner, CT and MRI acquisitions would occur simultaneously, and would be inherently registered in space and time. Alternatively, separately acquired CT and MRI scans can be fused to simulate an instantaneous acquisition. In this study, structural coupling and compressive sensing techniques are combined to unify CT and MRI reconstructions. A bidirectional image estimation method was proposed to connect images from different modalities. Hence, CT and MRI data serve as prior knowledge to each other for better CT and MRI image reconstruction than what could be achieved with separate reconstruction.

Significance: Combined CT-MRI imaging has the potential for improved results in existing preclinical and clinical applications, as well as opening novel research directions for future applications.

Results: Our integrated reconstruction methodology is demonstrated with numerical phantom and real-dataset-based experiments, and has yielded promising results.

Fig. 1

Comparison between CT and MRI images. (a) and (b) are two well-registered CT and MRI images. They are normalized into [0, 1]. (c, d) The line profiles along the white lines in (a) and (b) respectively. (e) The joint histogram of (a) and (b).

Fig. 2

Structural coupling for image estimation. Any given MRI patch p_MRI can be linearly represented with similar patches in T_MRI . Then, the corresponding CT patch p_CT can be linearly represented by the corresponding patches in T_CT with the same weighting factors $\left\{w_i\right\}$ as used for representing p_MRI.

Fig. 3

Datasets for testing CT-MRI reconstruction. The ground truth CT and MRI images in (a) mNCAT, (b) VHP, and (c) porcine experiments are shown in the first two columns respectively. The third column renders the registration results.

Fig. 4

Examples of CT and MRI datasets deformation. First, the transforms for CT and MRI datasets are produced based on reconstructed CT and MRI images and the prior CT and MRI datasets. Then, the transforms are applied to the CT and MRI datasets respectively, and new CT and MRI images are generated as improved guesses.

Fig. 5

Low magnetic field measurements in the MRI sub-system. Sampling patterns in the k-space for (a) mNCAT, (b) VHP, and (c) porcine experiments with undersampling rates of 92.5%, 82.7% and 89.0% respectively.

Fig. 6

Results of the mNCAT simulation. (a) and (b) are CT images using TV-based and simultaneous CT-MRI reconstructions, respectively. (c) and (d) are reconstructed MR images using the TV-based and CT-MRI method, respectively. (e-h) are the corresponding residual errors relative to ground truths for each reconstruction in the first row. (a-d) are displayed in [0, 1], and (e-h) in [−0.15, 0.15].

Fig. 7

Analysis on the simultaneous CT-MRI reconstruction with respect to patch size ($\sqrt{p_n}$) , relaxation parameter (α) and iteration index (k) in the mNCAT experiment. (a) RMSE quantifies the differences between the reconstructed and ground truth images with respective to various patch sizes $\sqrt{p_n}$ . (b) RMSE quantifies the differences between the reconstructed and ground truth images with respective to various relaxation parameter values α . (c) RMSE quantifies intermediate results as a function of the iteration index k ($\sqrt{p_n}=5$).

Fig. 8

Analysis on the simultaneous CT-MRI reconstruction with respect to various registration errors (Δx, Δy) and noise levels. (a-b) RMSE quantifies the differences between the reconstructed and ground truth images with respective to various registration errors between CT and MRI images. (c-d) RMSE quantifies the differences between the reconstructed and ground truth images at different noise levels.

Fig. 9

Results of VHP experiment. (a) and (b) are CT images using TV-based and simultaneous CT-MRI reconstructions, respectively. (c) and (d) are reconstructed MR images using the TV-based and CT-MRI method, respectively. (e-h) are the corresponding residual errors relative to ground truths for each reconstruction in the first row. (a-d) are displayed in [0, 1], and (e-h) in [−0.2, 0.2].

Fig. 10

Comparison over local regions in the VHP experiment. Local enlarged views of (a, d) the ground truth images, (b, e) reconstructed images using the TV-based method, and (c, f) reconstructed images using the proposed simultaneous CT-MRI method.

Fig. 11

Analysis on the simultaneous CT-MRI reconstruction with respect to patch size ($\sqrt{p_n}$) and iteration index in VHP experiment. (a) RMSE quantifies the differences between the reconstructed and ground truth images with respective to various patch sizes $\sqrt{p_n}$ . (b) RMSE quantifies intermediate results as a function of the iteration index k ($\sqrt{p_n}=15$).

Fig. 12

Results in the porcine experiment. (a) and (b) are CT images using TV-based and simultaneous CT-MRI reconstructions, respectively. (c) and (d) are reconstructed MR images using the TV-based and CT-MRI method, respectively. (e-h) are the corresponding residual errors relative to ground truths for each reconstruction in the first row. (a-d) are displayed in [0, 1], and (e-f) in [−0.3, 0.3], (g-h) in [−0.2, 0.2].

Fig. 13

Comparison of local regions in the porcine experiment. Local enlarged views of (a, d) the ground truth images, (b, e) reconstructed images using the TV-based method, and (c, f) reconstructed images using the proposed simultaneous CT-MRI method (in (a-c), veins – black; arteries – white, which demonstrate an improved definition of small vascular structures).

Fig. 14

Analysis on the simultaneous CT-MRI reconstruction with respect to patch size ($\sqrt{p_n}$) and iteration index in porcine experiment. (a) RMSE quantifies the differences between the reconstructed and ground truth images with respective to various patch sizes $\sqrt{p_n}$ . (b) RMSE quantifies intermediate results as a function of the iteration index k ($\sqrt{p_n}=15$).

Fig. 15

Quantitative summary of the mNCAT, VHP and porcine experiments. (a) RMSE and (b) SSIM quantify the differences between the reconstructed and ground truth images.