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

Abstract

In medical and industrial applications of computed tomography (CT) imaging, limited by the scanning environment and the risk of excessive X-ray radiation exposure imposed to the patients, reconstructing high quality CT images from limited projection data has become a hot topic. X-ray imaging in limited scanning angular range is an effective imaging modality to reduce the radiation dose to the patients. As the projection data available in this modality are incomplete, limited-angle CT image reconstruction is actually an ill-posed inverse problem. To solve the problem, image reconstructed by conventional filtered back projection (FBP) algorithm frequently results in conspicuous streak artifacts and gradual changed artifacts nearby edges. Image reconstruction based on total variation minimization (TVM) can significantly reduce streak artifacts in few-view CT, but it suffers from the gradual changed artifacts nearby edges in limited-angle CT. To suppress this kind of artifacts, we develop an image reconstruction algorithm based on ℓ 0 gradient minimization for limited-angle CT in this paper. The ℓ 0-norm of the image gradient is taken as the regularization function in the framework of developed reconstruction model. We transformed the optimization problem into a few optimization sub-problems and then, solved these sub-problems in the manner of alternating iteration. Numerical experiments are performed to validate the efficiency and the feasibility of the developed algorithm. From the statistical analysis results of the performance evaluations peak signal-to-noise ratio (PSNR) and normalized root mean square distance (NRMSD), it shows that there are significant statistical differences between different algorithms from different scanning angular ranges (p<0.0001). From the experimental results, it also indicates that the developed algorithm outperforms classical reconstruction algorithms in suppressing the streak artifacts and the gradual changed artifacts nearby edges simultaneously.

Wavelet tight frame and prior image-based image reconstruction from limited-angle projection data

“…Because the sequence f n+1 and f n are generated by our algorithm, therefore, f n+1 ∈ Ω and f n ∈ Ω, adding (43), (44) and (45) together, and using the fact that…”

“…In [10], the authors proposed an anisotropic TV reconstruction algorithm. Although these methods reduce the limited-angle artifacts near edges, the edges of object are still distorted [44].…”

Sparse View CT Image Reconstruction Based on Total Variation and Wavelet Frame Regularization

“…As a kind of sparse representation, the wavelet frame have been successfully applied to CT reconstruction [28]- [32]. Especially, a high quality reconstruction image can be obtained by the methods based on variational and wavelet frame regularization for limited-angle CT reconstruction [29], [30]. However, there will be pseudo-Gibbs phenomenon in the reconstructed image.…”

An Algorithm ofl1-Norm andl0-Norm Regularization Algorithm for CT Image Reconstruction from Limited Projection

“…The l 0 -norm of an image vector, defined as the number of its nonzero elements, measures the sparsity of a vector appropriately. So the l 0 -norm-based regularization for CT represents the sparsity of the gradient image better than the l 1 -norm-based regularization and preserves the edge while suppressing the streak artifacts [13]. However, the l 0 -norm is a nonconvex function and the l 0 -norm regularization problem is NP hard [14].…”