Reconstructing a 3D Medical Image from a Few 2D Projections Using a B-Spline-Based Deformable Transformation

Hui Yan () and Jianrong Dai
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Hui Yan: Department of Radiation Oncology, National Cancer Center/National Clinical Research Center for Cancer/Cancer Hospital, Chinese Academy of Medical Sciences and Peking Union Medical College, Beijing 100021, China
Jianrong Dai: Department of Radiation Oncology, National Cancer Center/National Clinical Research Center for Cancer/Cancer Hospital, Chinese Academy of Medical Sciences and Peking Union Medical College, Beijing 100021, China

Mathematics, 2022, vol. 11, issue 1, 1-12

Abstract: (1) Background: There was a need for 3D image reconstruction from a series of 2D projections in medical applications. However, additional exposure to X-ray projections may harm human health. To alleviate it, minimizing the projection numbers is a solution to reduce X-ray exposure, but this would cause significant image noise and artifacts. (2) Purpose: In this study, a method was proposed for the reconstruction of a 3D image from a minimal set of 2D X-ray projections using a B-spline-based deformable transformation. (3) Methods: The inputs of this method were a 3D image which was acquired in previous treatment and used as a prior image and a minimal set of 2D projections which were acquired during the current treatment. The goal was to reconstruct a new 3D image in current treatment from the two inputs. The new 3D image was deformed from the prior image via the displacement matrixes that were interpolated by the B-spline coefficients. The B-spline coefficients were solved with the objective function, which was defined as the mean square error between the reconstructed and the ground-truth projections. In the optimization process the gradient of the objective function was calculated, and the B-spline coefficients were then updated. For the acceleration purpose, the computation of the 2D and 3D image reconstructions and B-spline interpolation were implemented on a graphics processing unit (GPU). (4) Results: When the scan angles were more than 60°, the image quality was significantly improved, and the reconstructed image was comparable to that of the ground-truth image. As the scan angles were less than 30°, the image quality was significantly degraded. The influence of the scan orientation on the image quality was minor. With the application of GPU acceleration, the reconstruction efficiency was improved by hundred times compared to that of the conventional CPU. (5) Conclusions: The proposed method was able to generate a high-quality 3D image using a few 2D projections, which amount to ~ 20% of the total projections required for a standard image. The introduction of the B-spline-interpolated displacement matrix was effective in the suppressing noise in the reconstructed image. This method could significantly reduce the imaging time and the radiation exposure of patients under treatment.

Keywords: image reconstruction; B-spline; deformable; graphics processing unit (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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