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.