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ℓ0 Gradient Minimization Based Image Reconstruction for Limited-Angle Computed Tomography.

Wei Yu¹, Li Zeng²

¹School of Biomedical Engineering, Hubei University of Science and Technology, Xianning, China; Engineering Research Center of Industrial Computed Tomography Nondestructive Testing of the Education Ministry of China, Chongqing University, Chongqing, China.

|July 10, 2015

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This study introduces a new ℓ0 gradient minimization algorithm for limited-angle computed tomography (CT) image reconstruction. The novel method effectively suppresses streak and edge artifacts, improving image quality in low-dose X-ray imaging.

Area of Science:

Medical imaging
Computational imaging
Image reconstruction

Background:

Limited projection data in computed tomography (CT) imaging poses challenges due to scanning constraints and radiation exposure risks.
Conventional filtered back projection (FBP) and total variation minimization (TVM) algorithms struggle with artifacts like streaks and edge distortions in limited-angle CT.
Developing robust reconstruction methods is crucial for high-quality CT imaging in medical and industrial applications.

Purpose of the Study:

To develop a novel image reconstruction algorithm for limited-angle CT that effectively suppresses both streak and gradual edge artifacts.
To address the ill-posed nature of limited-angle CT reconstruction using a regularization approach.
To improve the quality of CT images reconstructed from incomplete projection data.

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Main Methods:

An image reconstruction algorithm based on ℓ0 gradient minimization was developed for limited-angle CT.
The ℓ0-norm of the image gradient was utilized as the regularization function within the reconstruction model.
The optimization problem was decomposed into sub-problems solved via alternating iterative methods.

Main Results:

Numerical experiments demonstrated the efficiency and feasibility of the proposed ℓ0 gradient minimization algorithm.
Statistical analysis (PSNR, NRMSD) confirmed significant differences in performance across algorithms and angular ranges (p<0.0001).
The developed algorithm showed superior performance in simultaneously suppressing streak artifacts and gradual edge artifacts compared to classical methods.

Conclusions:

The ℓ0 gradient minimization algorithm offers a significant advancement in limited-angle CT image reconstruction.
This method effectively mitigates common artifacts, leading to enhanced image quality in low-dose CT scenarios.
The findings support the use of this algorithm for improving diagnostic accuracy and reducing patient radiation exposure in CT imaging.