# American Institute of Mathematical Sciences

June  2019, 13(3): 449-460. doi: 10.3934/ipi.2019022

## CT image reconstruction on a low dimensional manifold

 1 Biomedical Imaging Center, Department of Biomedical Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180, USA 2 School of Mathematics, Sun Yat-sen University, Guangzhou 510275, China 3 GE Healthcare Technologies, Waukesha, WI 53188, USA 4 Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY 12180, USA

* Corresponding authors: Rongjie Lai

Received  January 2018 Revised  January 2019 Published  March 2019

Fund Project: W. Cong, G. Wang and Q. Yang's work is partially supported by the National Institutes of Health Grant NIH/NIBIB R01 EB016977 and U01 EB017140. R. Lai's work is partially supported by the National Science Foundation NSF DMS-1522645 and an NSF CAREER Award DMS-1752934

The patch manifold of a natural image has a low dimensional structure and accommodates rich structural information. Inspired by the recent work of the low-dimensional manifold model (LDMM), we apply the LDMM for regularizing X-ray computed tomography (CT) image reconstruction. This proposed method recovers detailed structural information of images, significantly enhancing spatial and contrast resolution of CT images. Both numerically simulated data and clinically experimental data are used to evaluate the proposed method. The comparative studies are also performed over the simultaneous algebraic reconstruction technique (SART) incorporated the total variation (TV) regularization to demonstrate the merits of the proposed method. Results indicate that the LDMM-based method enables a more accurate image reconstruction with high fidelity and contrast resolution.

Citation: Wenxiang Cong, Ge Wang, Qingsong Yang, Jia Li, Jiang Hsieh, Rongjie Lai. CT image reconstruction on a low dimensional manifold. Inverse Problems & Imaging, 2019, 13 (3) : 449-460. doi: 10.3934/ipi.2019022
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##### References:
The patch manifold of a CT image (left) and the corresponding dimension function of the patch manifold with patch size $16\times 16$ (right)
Comparison of image reconstruction. (a) Ground truth CT images, (b) the reconstructed image using the LDMM-based method, and (c) the reconstructed image using SART with TV
Profiles of reconstructed image. (a) The profiles along the vertical midlines in the phantom and image reconstructed by LDMM-based reconstruction method, (b) the profiles along the horizontal midlines in the phantom and image reconstructed by LDMM-based reconstruction method. (c) The profiles along the vertical midlines in the phantom and image reconstructed by SART+TV reconstruction method, and (d) the profiles along the horizontal vertical midlines in the phantom and image reconstructed by SART+TV reconstruction method
The sinogram simulated from CatSim
The sinogram measured from a clinical x-ray CT scanner
Comparison of CT reconstruction. (a) Ground truth CT images, (b) the reconstructed image using the LDMM-based image reconstruction method, and (c) the reconstructed image using SART with TV
Comparison of CT image reconstructions from clinical CT raw data. (a) The reconstructed image using the LDMM-based method, (b) the reconstructed image using SART with TV, and (c) the reconstructed image using FPB
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