An iterative method for backward time‐fractional diffusion problem

The aim of this work is to solve the backward problem for a time‐fractional diffusion equation with variable coefficients in a general bounded domain. The problem is ill‐posed in L ² norm sense. An iteration scheme is proposed to obtain a regularized solution. Two kinds of convergence rates are obtained using an a priori regularization parameter choice rule and an a posteriori regularization parameter choice rule. Numerical examples in one‐dimensional and two‐dimensional cases are provided to show the effectiveness of the proposed methods. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 2029–2041, 2014     

Optimal capital allocations to interdependent actuarial risks

This paper further studies the capital allocation concerning mutually interdependent random risks. In the context of exchangeable random risks, we establish that risk-averse insurers incline to evenly distribute the total capital among multiple risks. For risk-averse insurers with decreasing convex loss functions, we prove that more capital should be allocated to the risk with the larger reversed hazard rate when risks are coupled by an Archimedean copula. Also, sufficient conditions are developed to exclude the worst capital allocations for random risks with some specific Archimedean copulas.     

Bregman iterative model using the G-norm

In this paper, we analyze the Bregman iterative model using the G-norm. Firstly, we show the convergence of the iterative model. Secondly, using the source condition and the symmetric Bregman distance, we consider the error estimations between the iterates and the exact image both in the case of clean and noisy data. The results show that the Bregman iterative model using the G-norm has the similar good properties as the Bregman iterative model using the L2-norm.     

An inverse problem for space‐fractional backward diffusion problem

In this paper, an inverse problem for space‐fractional backward diffusion equation, which is highly ill‐posed, is considered. This problem is obtained from the classical diffusion equation by replacing the second‐order space derivative with a Riesz–Feller derivative of order α ∈ (0,2]. We show that such a problem is severely ill‐posed, and further present a simplified Tikhonov regularization method to deal with this problem. Convergence estimate is presented under a priori choice of regularization parameter. Numerical experiments are given to illustrate the accuracy and efficiency of the proposed method. Copyright © 2013 John Wiley & Sons, Ltd.     

Multi-parameter Tikhonov Regularization—An Augmented Approach

We study multi-parameter regularization （multiple penalties） for solving linear inverse problems to promote simultaneously distinct features of the sought-for objects. We revisit a balancing principle for choosing regularization parameters from the viewpoint of augmented Tikhonov regularization, and derive a new parameter choice strategy called the balanced discrepancy principle. A priori and a posteriori error estimates are provided to theoretically justify the principles, and numerical algorithms for efficiently implementing the principles are also provided. Numerical results on deblurring are presented to illustrate the feasibility of the balanced discrepancy principle.     

Properties and Iterative Methods for the Lasso and Its Variants

The lasso of Tibshirani （1996） is a least-squares problem regularized by the l1 norm. Due to the sparseness promoting property of the l1 norm, the lasso has been received much attention in recent years. In this paper some basic properties of the lasso and two variants of it are exploited. Moreover, the proximal method and its variants such as the relaxed proximal algorithm and a dual method for solving the lasso by iterative algorithms are presented.     

IDENTIFYING AN UNKNOWN SOURCE IN SPACE-FRACTIONAL DIFFUSION EQUATION

In this paper, we identify a space-dependent source for a fractional diffusion equation. This problem is ill-posed, i.e., the solution （if it exists） does not depend continuously on the data. The generalized Tikhonov regularization method is proposed to solve this problem. An a priori error estimate between the exact solution and its regularized approximation is obtained. Moreover, an a posteriori parameter choice rule is proposed and a stable error estimate is also obtained, Numerical examples are presented to illustrate the validity and effectiveness of this method.     

CONVERGENCE ANALYSIS OF THE LOPING OS-EM ITERATIVE VERSION OF THE CIRCULAR RADON TRANSFORM

The loping OS-EM iteration is a numerically efficient regularization method for solving ill-posed problems. In this article we investigate the loping OS-EM iterative method in connection with the circular Radon transform. We show that the proposed method converges weakly for the noisy data. Numerical tests are presented for a linear problem related to photoacoustic tomography.     

功率放大器失真问题研究及预失真建模

电子器件中的功率放大器常常伴随着非线性失真效应.为解决此类非线性失真问题,通过研究无记忆和有记忆功放的失真特性,运用最小二乘法来构建多种形式的特性拟合函数,在选择了效果较好的特性拟合函数基础上,根据实际约束条件进行预失真模型的建立,使失真处理后的输出信号趋于线性,最后从信号的功率谱密度的角度出发检验预失真模型的补偿效果,证明模型具有较好的可行性和准确性.