IPI
Existence and convergence analysis of $\ell_{0}$ and $\ell_{2}$ regularizations for limited-angle CT reconstruction
Chengxiang Wang Li Zeng Wei Yu Liwei Xu

In some practical applications of computed tomography (CT) imaging, the projections of an object are obtained within a limited-angle range due to the restriction of the scanning environment. In this situation, conventional analytic algorithms, such as filtered backprojection (FBP), will not work because the projections are incomplete. An image reconstruction algorithm based on total variation minimization (TVM) can significantly reduce streak artifacts in sparse-view reconstruction, but it will not effectively suppress slope artifacts when dealing with limited-angle reconstruction problems. To solve this problem, we consider a family of image reconstruction model based on $\ell_{0}$ and $\ell_{2}$ regularizations for limited-angle CT and prove the existence of a solution for two CT reconstruction models. The Alternating Direction Method of Multipliers (ADMM)-like method is utilized to solve our model. Furthermore, we prove the convergence of our algorithm under certain conditions. Some numerical experiments are used to evaluate the performance of our algorithm and the results indicate that our algorithm has advantage in suppressing slope artifacts.

keywords: Inverse problems computed tomography image reconstruction wavelet transform 0 regularization
IPI
The reciprocity gap method for a cavity in an inhomogeneous medium
Fang Zeng Xiaodong Liu Jiguang Sun Liwei Xu
We consider an interior inverse medium problem of reconstructing the shape of a cavity. Both the measurement locations and point sources are inside the cavity. Due to the lack of a priori knowledge of physical prosperities of the medium inside the cavity and to avoid the computation of background Green's functions, the reciprocity gap method is employed. We prove the related theory and present some numerical examples for validation.
keywords: inhomogeneous medium reciprocity gap method. Interior inverse scattering problem

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