Reference-guided CS-MRI with Gradient Orientation Priors
Xi Peng1, Shanshan Wang1, Qingyong Zhu1, and Dong Liang1

1Shenzhen Institutes of Advanced Technology, Shenzhen, China, People's Republic of

### Synopsis

In various MR applications, a pre-scan is usually practicable that extra morphology information can be extracted from the reference image. However, with a reference image obtained from a different contrast mechanism, the signal variation in the reference may differ from that in the target image. In this work, we propose to exploit gradient orientation information, which is closely related to the anatomical structures but less dependent on the image contrast, to enable superior CS-based reconstruction. The proposed method was validated using multi-scan experiment data and is shown to provide high speed and high quality imaging.

### INTRODUCTION

The theory of Compressed sensing (CS) provides a systematic framework for MR image reconstruction from under-sampled k-space data. Moreover, in various MR applications, a pre-scan is usually practicable that a high-spatial resolution reference image can be easily obtained. Thus, extra morphology information can be extracted from the reference image [1-7], provided that the reference and the target image share similar anatomy. However, with a reference image obtained using a different contrast mechanism, the signal variation in the reference may differ from that in the target image. To this end, signal intensity involved reference prior may no longer be optimal. In this work, we propose to exploit directional information, named gradient orientation priors (GOP), which is closely related to the anatomical structures but less dependent on the image contrast. Specifically, we regularize the tangent vector in the target image to be perpendicular to the corresponding normal vector in the reference image over all spatial locations. The proposed method was validated using multi-scan experiment data and is shown to provide high speed and high quality imaging.

### THEORY AND METHOD

Firstly, we define gradient orientation as: $\triangledown\rho=[\rho_x, \rho_y]$, where $\rho_x$ and $\rho_y$ are the finite difference on the first and second coordinates respectively. $\triangledown\rho$ actually represents the tangent vector at certain spatial location. Further, the normal vector at the corresponding location can be written as: $\xi_\rho=[-\rho_y, \rho_x]$ with $<\triangledown\rho,\xi_\rho>=0$. $<\cdot,\cdot>$ denotes vector inner product. If we assume the anatomy of a reference image $v$ is well aligned with that of the target image, we would expect: $<\triangledown\rho,\xi_v/|\triangledown v|>\approx0$. Note that in order to exclude the effect of reference contrast, we normalized the normal vector in the reference image to solely preserve directional information. Finally, to impose the anatomical alignment constraint of the reference and the target image, we simply regularize the above vector inner product over all spatial locations. The proposed CS-MRI problem with gradient orientation priors (CS-GOP) can be formulated as: $$\underset{\rho}{\operatorname{argmin}}||F_u\rho-d||_2^2+\lambda_1||\Psi\rho||_1+\lambda_2\sum_{FOV} ||<\triangledown\rho,\xi_v/|\triangledown v|>||_2^2$$ where $\lambda_1$ and $\lambda_2$ are regularization parameters controlling the strength of image sparsity and gradient orientation priors, respectively. To solve this optimization problem, we used the standard nonlinear conjugate gradient method. It is worth noting that though only two orientations are considered in this work, generalization to multiple orientations is straight forward.

### EXPERIMENT AND RESULT

Here we used a multi scan experiment to justify the feasibility of the proposed technique when the reference and the target images come from different protocols. Specifically, we used a pre-acquired proton-density weighted brain image (TR=5000 ms, TE=9.7 ms) as a reference to reconstruct a subsequently scanned T1 weighted (TR=2000 ms, TE=9.7 ms) image, both of which were acquired using a turbo spin echo sequence (matrix size=384×324, FOV=230×187 $\text{mm}^2$, slice thickness=5.0 mm, bandwidth=123.26 Hz/pixel). Variable density random undersampling along the phase encoding direction were adopted to generate the retrospectively undersampled k-space data. Complex Gaussian noise was added to synthesize a noisy case of 25dB SNR. To evaluate the proposed method, we conducted comparisons with the conventional CS using total variation (CS-TV) and a weighed-L1 CS (CS-wL1) where the weights were calculated from the reference [3]. Reconstruction results and relative errors are shown in Fig. 1 and Fig. 2. A central region was zoomed in and superimposed on the original image for better visualization. As can be seen, severe aliasing artifacts occur in the CS-TV method at reduction factor R=3 and 4. With anatomical weights incorporated, the artifacts are alleviated but still obvious and unacceptable. The proposed technique provide considerable promising results that the aliasing artifacts are significantly suppressed and more image details are preserved even at R=4.

### CONCLUSION

In this paper, we propose a reference-guided CS-MRI reconstruction method using gradient orientation priors which could be more robust when the signal variation in the target and the reference images is discrepant. Experiments have showed that the proposed technique exhibits superior reconstruction performance to conventional CS-based methods, providing considerable potential in MR applications where a reference image is available.

### Acknowledgements

We would like to acknowledge National Natural Science Foundation of China under Grants 11301508, 81120108012, 81328013, 61471350, the Natural Science Foundation of Guangdong 2015A020214019, 2015A030310314, 2015A030313740 and the Basic Research Program of Shenzhen JCYJ20150630114942318, JCYJ20140610152828678, JCYJ20140610151856736.

### References

[1] Wang Q, IEEE ISBI 2013. pp. 290–293. [2] Babacan SD, IEEE EMBS 2011. pp. 5718–5721. [3] Haldar JP, MRM 2008. pp. 810–818. [4] Liang ZP, IEEE TMI 1994. pp. 677-686. [5] Liang ZP, IEEE TMI 2003. pp. 1026-1030. [6] Ji X, IEEE ISBI 2002. pp. 789-792. [7] Ji J, IEEE ISBI 2008. pp. 789-792.

### Figures

Fig. 1. Reconstruction results of CS-TV, CS-wL1 and CS-GOP at reduction factors R= 2, 3 and 4. A local region was zoomed in and superimposed on the original image for better visualization.

Fig. 2. Reconstruction errors of CS-TV, CS-wL1 and CS-GOP methods with respect to reduction factors in the moderate (left) and low SNR (right) cases.

Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)
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