Limited-angle cone-beam computed tomography image reconstruction by total variation minimization and piecewise-constant modification

Abstract

Because of x-ray dose considerations or practical mechanical restrictions, it may be interesting for some applications to perform limited-angle scanning. So the limitedangle problem is of practical significance in computed tomography (CT). Furthermore, it is an ill-posed problem. Total variation minimization (TVM) and projection on convex sets (POCS) based iterative reconstruction algorithm is comparatively valid for this undersampling CT reconstruction problem and can obtain comparatively good performance. But the reconstruction images have artifacts with gradual change gray nearby edges. In this paper, a simple but efficient method to eliminate such artifacts during the reconstruction is proposed. Based on the same assumption of the TVM algorithm, for the object whose density distribution is approximate piecewise-constant, we develop and investigate an improved iterative reconstruction algorithm for volume image reconstruction from limited-angle cone-beam scan, which is referred to as piecewise-constant modification TVM-POCS (PM-TVM-POCS) algorithm. The grays of voxels with gradually changed gray artifacts are modified in the TVM-POCS iteration process by the piecewiseconstant modification algorithm which is regarded as a "collapse" process, and gradually approaches the true piecewise-constant image. The results of simulation experiments show that the presented modification algorithm can improve the quality of the reconstructed image obviously and it is steady to noise. This modification algorithm can also be applied to other reconstruction problems which have artifacts with gradual change gray.

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…”

“…A high quality reconstructed image can be obtained using ASD-POCS algorithm for the sparse-view sampling over 360 0 . However, the limited-angle artifacts will be presented near edges of reconstructed image when the scanning angular range is seriously limited [45]. To overcome these problems, some authors have improved the CT reconstruction algorithm with TV.…”

Quantitative study on exact reconstruction sampling condition by verifying solution uniqueness in limited-view CT

“…The existing sufficient or necessary conditions for exact reconstruction have not deepened insight into the mathematical or physical essence of the reconstruction model. A precise mathematical study on sampling condition would help to develop a more efficient algorithm for the limited-view problem, which is inevitable to the issue of reducing radiation dose and of restricted scanning geometry [28][29]. Furthermore, the question of the suitable lower bound of the scanning range for limited-view exact reconstruction has not been answered until now.…”

Existence and convergence analysis of <inline-formula><tex-math id="M1">\begin{document} $\ell_{0}$ \end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M2">\begin{document} $\ell_{2}$ \end{document}</tex-math></inline-formula> regularizations for limited-angle CT reconstruction

“…The ASD-POCS algorithm can obtain a good reconstructed image from sparse angular sampling over 360 0 and suppress streak artifacts. However, the reconstructed image suffers from slope artifacts near the edges of the object (see Figure 4 and Figure 6 ) when the scanning angular range is seriously limited and less than 180 0 (such as 100 0 or 130 0 ) [64]. Some scholars have advanced the conventional TV based image reconstruction algorithm to further improve the quality of CT images for limited-angle tomography [42,43,15].…”