Wavelet tight frame and prior image-based image reconstruction from limited-angle projection data
Chengxiang Wang Li Zeng Yumeng Guo Lingli Zhang

The limited-angle projection data of an object, in some practical applications of computed tomography (CT), are obtained due to the restriction of scanning condition. In these situations, since the projection data are incomplete, some limited-angle artifacts will be presented near the edges of reconstructed image using some classical reconstruction algorithms, such as filtered backprojection (FBP). The reconstructed image can be fine approximated by sparse coefficients under a proper wavelet tight frame, and the quality of reconstructed image can be improved by an available prior image. To deal with limited-angle CT reconstruction problem, we propose a minimization model that is based on wavelet tight frame and a prior image, and perform this minimization problem efficiently by iteratively minimizing separately. Moreover, we show that each bounded sequence, which is generated by our method, converges to a critical or a stationary point. The experimental results indicate that our algorithm can efficiently suppress artifacts and noise and preserve the edges of reconstructed image, what's more, the introduced prior image will not miss the important information that is not included in the prior image.

keywords: Inverse problems image reconstruction wavelet transform $\ell_0$ regularized prior information
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
Multi-period portfolio optimization in a defined contribution pension plan during the decumulation phase
Chuangwei Lin Li Zeng Huiling Wu

This paper studies a multi-period portfolio selection problem for retirees during the decumulation phase. We set a series of investment targets over time and aim to minimize the expected losses from the time of retirement to the time of compulsory annuitization by using a quadratic loss function. A target greater than the expected wealth is given and the corresponding explicit expressions for the optimal investment strategy are obtained. In addition, the withdrawal amount for daily life is assumed to be a linear function of the wealth level. Then according to the parameter value settings in the linear function, the withdrawal mechanism is classified as deterministic withdrawal, proportional withdrawal or combined withdrawal. The properties of the investment strategies, targets, bankruptcy probabilities and accumulated withdrawal amounts are compared under the three withdrawal mechanisms. Finally, numerical illustrations are presented to analyze the effects of the final target and the interest rate on some obtained results.

keywords: Defined-contribution pension scheme decumulation phase income drawdown option quadratic loss function portfolio selection optimization
Error bounds and stability in the $l_{0}$ regularized for CT reconstruction from small projections
Chengxiang Wang Li Zeng
Due to the restriction of the scanning environment and the energy of X-ray, few projections of an object can be obtained in some practical applications of computed tomography (CT). In these situations, the projection data are incomplete and inconsistent, and the conventional analytic algorithm such as filtered backprojection (FBP) algorithm will not work. The streak artifacts can be significantly reduced in few-view reconstruction if the total variation minimization (TVM) based CT reconstruction algorithm is used. However, in the premise of preserving the resolution of image, it will not effectively suppress slope artifacts and metal artifacts when dealing with some few-view of the limited-angle reconstruction problems. To solve this problem, we focus on the image reconstruction algorithm base on $\ell_{0}$ regularized of wavelet coefficients. In this paper, the error bound between the reference or desire image and the reconstructed result, and the stability of solution were shown in theoretical and experimental, a reconstruction experiment on metal laths from few-view of the limited-angle projections was given. The experimental results indicate that this algorithm outperforms classical CT reconstruction algorithms in preserving the resolution of reconstructed image and suppressing the metal artifacts.
keywords: image reconstruction $\ell_{0}$ regularized. computed tomography Inverse problems wavelet transform

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