Nonlocal regularization based on DT-CWT for WMSN video image iterative reconstruction

The prior knowledge of signal is the previous condition of image compressed sensing reconstruction. In order to improve the quality of the priors except for image sparsity, this paper proposes a new model of video image reconstruction. The texture is the important visual feature of video image as a result of its repeat, leading to image global geometrical structures. The nonlocal idea comes from image self-familiar and can represent image detail features from the geometrical point of view. Therefore, the texture geometrical feature of video image is researched, and we take advantage of dual-tree complex wavelet transform to portray the sparsity representation regularization of the texture. What is more, global constrained regularization is constructed with the help of the nonlocal idea. On the basis of the two regularizations above, a new reconstruction model of video image compressed sensing is proposed, which not only preserves the sparsity prior knowledge of image but also improves the quality of prior knowledge of image by promoting geometrical structure. Iterative shrinkage thresholding algorithm is adopted to solve the model leading to a both simple and quick iterative algorithm. Numerical experiments show that our method is efficient for video image recovery, especially preserving the global details of the original video image.     

Image-guided regularization level set evolution for MR image segmentation and bias field correction

Magnetic resonance (MR) image segmentation is a crucial step in surgical and treatment planning. In this paper, we propose a level-set-based segmentation method for MR images with intensity inhomogeneous problem. To tackle the initialization sensitivity problem, we propose a new image-guided regularization to restrict the level set function. The maximum a posteriori inference is adopted to unify segmentation and bias field correction within a single framework. Under this framework, both the contour prior and the bias field prior are fully used. As a result, the image intensity inhomogeneity can be well solved. Extensive experiments are provided to evaluate the proposed method, showing significant improvements in both segmentation and bias field correction accuracies as compared with other state-of-the-art approaches.     

二维电磁逆散射问题的时域高斯-牛顿反演算法

为了直接利用超宽带(UWB)时域测量数据,同时重建二维(2D)目标(OI)的介电常数和电导率,本文将频域高斯-牛顿反演(GNI)算法发展为时域形式.迭代重建过程中,正问题由时域有限差分(FDTD)法求解,而逆问题的病态特性用自适应正则化技术抑制.四类数值算例中,噪声影响均被考虑,仿真结果初步证实了改进算法的可行性和鲁棒性.重建图像呈现超分辨率(SR),有望应用到早期乳腺癌检测等实际问题中.     

基于空间自适应非凸正则项全变差相干斑噪声抑制

全变差正则化方法是相干斑噪声抑制研究的热点.非凸正则项能够更好地保持图像的边缘、纹理细节信息;空间自适应正则化参数可以根据像素点所在的区域,合理地控制噪声抑制程度,从而提高噪声抑制效果.本文结合非凸正则项和空间自适应正则化参数提出了一种新的全变差相干斑噪声抑制模型,并且给出了一种模型求解的数值算法.数值试验结果表明该模型能够获得更好的相干斑噪声抑制效果.     

基于Tikhonov正则参量后验选择策略的PCS颗粒粒度反演方法

采用基于Morozov偏差原理的后验策略来选择最优正则参量,并采用此方法对单峰和多峰分布颗粒系的模拟电场自相关函数进行了反演,结果表明,对于单峰颗粒体系,当电场自相关函数的扰动误差小于0.05时,反演得到的峰值准确,当电场自相关函数的扰动误差大于0.05时,反演得到的峰值偏离所模拟的颗粒粒径.正则参量初始值在0.000 02～2范围内,在反演所得的峰值准确的基础上,正则参量初始值越小,反演得到的分布宽度越窄.收敛误差在0.000 05～50范围内,在保持反演结果稳定的基础上,收敛误差取值越大,反演得到的分布宽度越窄.对于多峰颗粒体系,当颗粒系中的颗粒粒径差别较小时,峰值向平均值偏移,当颗粒系中的颗粒粒径差别较大时,小颗粒粒径分布以噪音的形式出现.     

Properties of positive solutions to a class of four-point boundary value problem of Caputo fractional differential equations with a parameter

In this paper, by using fixed point theorems of concave operators in partial ordering Banach spaces, we establish the existence and uniqueness of positive solutions to a class of four-point boundary value problem of Caputo fractional differential equations for any given parameter. Moreover, we present some pleasant properties of positive solutions to the boundary value problem dependent on the parameter. In the end, two examples are given to illustrate our main results.     

Extension of GKB‐FP algorithm to large‐scale general‐form Tikhonov regularization

In a recent paper an algorithm for large‐scale Tikhonov regularization in standard form called GKB‐FP was proposed and numerically illustrated. In this paper, further insight into the convergence properties of this method is provided, and extensions to general‐form Tikhonov regularization are introduced. In addition, as alternative to Tikhonov regularization, a preconditioned LSQR method coupled with an automatic stopping rule is proposed. Preconditioning seeks to incorporate smoothing properties of the regularization matrix into the computed solution. Numerical results are reported to illustrate the methods on large‐scale problems. Copyright © 2013 John Wiley & Sons, Ltd.     

Embedded techniques for choosing the parameter in Tikhonov regularization

This paper introduces a new strategy for setting the regularization parameter when solving large‐scale discrete ill‐posed linear problems by means of the Arnoldi–Tikhonov method. This new rule is essentially based on the discrepancy principle, although no initial knowledge of the norm of the error that affects the right‐hand side is assumed; an increasingly more accurate approximation of this quantity is recovered during the Arnoldi algorithm. Some theoretical estimates are derived in order to motivate our approach. Many numerical experiments performed on classical test problems as well as image deblurring problems are presented. Copyright © 2014 John Wiley & Sons, Ltd.     

一类带非线性边界条件的非线性抛物方程的解的整体存在性

该文考虑带非线性边界条件的非线性抛物方程的正整体解的存在性与非存在性。通过使用上下解技巧，得到了所有正解整体存在的充分必要条件。作者所构造的上下解具有相同的形式且计算简便。     

Multiple Sign-Changing Solutions for Quasilinear Equations of Bounded Quasilinearity

The existence of an infinite sequence of sign-changing solutions are proved for a class of quasilinear elliptic equations under suitable conditions on the quasilinear coefficients and the nonlinearity■ where ? ? R~N is a bounded domain with smooth boundary, and we use■ The main interest of this paper is for the case of bounded quasilinearity bij. The result is proved by an elliptic regularization method involving truncations of both u and the gradient of u.