Convergence results of Landweber iterations for linear systems

The Landweber scheme is a method for algebraic image reconstructions. The convergence behavior of the Landweber scheme is of both theoretical and practical importance. Using the diagonalization of matrix, we derive a neat iterative representation formula for the Landweber schemes and consequently establish the convergence conditions of Landweber iteration. This work refines our previous convergence results on the Landweber scheme.     

基于TSP规划模型的碎纸片拼接复原问题研究

引入差异度指标描述碎纸片图像边缘的匹配程度,以差异度最小为目标建立TSP问题的数学模型,并按照指派模型求解。设计“按行聚类-行内排序”算法,以降低算法的时间复杂度;同时,对字符进行聚类分析,并利用模式识别技术降低拼接的错误率,减少人工干预;通过纵切、纵横切、双面的中英文碎纸片的复原,验证了拼接模型和算法的准确性和有效性。     

基于动态模态分解的长江口海表温度时空分布特征重构研究

河口近海海域的海表温度分布特征对于深入理解海洋热力、动力过程及海气相互作用等自然过程及综合效应具有重要意义。卫星数据重构是精确获取动态大面积海表温度数据的重要手段,采用非线性系统的动态模态分解（dynamic mode decomposition,DMD）数据分析方法,利用2003年1月至2016年7月的MODIS\SST数据,经剔除异常数据、填补空白数据后,重构了2016年8月至2019年12月长江口海洋表面温度数据,并评估了重构效果。研究结果表明,在时序数据充足的情况下,DMD算法能很好地解决动态系统的采样问题。DMD结合正交三角（orthogonal right triangular,QR）分解算法能有效重构长江口的海表温度数据,平均均方根误差（root mean square error,RMSE）为0.007 6。进一步分析发现,无论是DMD算法还是DMD结合QR分解算法,还原结果精度都较高。     

High‐order k‐exact WENO finite volume schemes for solving gas dynamic Euler equations on unstructured grids

This paper presents a family of High‐order finite volume schemes applicable on unstructured grids. The k‐exact reconstruction is performed on every control volume as the primary reconstruction. On a cell of interest, besides the primary reconstruction, additional candidate reconstruction polynomials are provided by means of very simple and efficient ‘secondary’ reconstructions. The weighted average procedure of the WENO scheme is then applied to the primary and secondary reconstructions to ensure the shock‐capturing capability of the scheme. This procedure combines the simplicity of the k‐exact reconstruction with the robustness of the WENO schemes and represents a systematic and unified way to construct High‐order accurate shock capturing schemes. To further improve the efficiency, an efficient problem‐independent shock detector is introduced. Several test cases are presented to demonstrate the accuracy and non‐oscillation property of the proposed schemes. The results show that the proposed schemes can predict the smooth solutions with uniformly High‐order accuracy and can capture the shock waves and contact discontinuities in high resolution. Copyright © 2011 John Wiley & Sons, Ltd.     

Optical diffraction tomography microscopy with transport of intensity equation using a light-emitting diode array

Optical diffraction tomography (ODT) is an effective label-free technique for quantitatively refractive index imaging, which enables long-term monitoring of the internal three-dimensional (3D) structures and molecular composition of biological cells with minimal perturbation. However, existing optical tomographic methods generally rely on interferometric configuration for phase measurement and sophisticated mechanical systems for sample rotation or beam scanning. Thereby, the measurement is suspect to phase error coming from the coherent speckle, environmental vibrations, and mechanical error during data acquisition process. To overcome these limitations, we present a new ODT technique based on non-interferometric phase retrieval and programmable illumination emitting from a light-emitting diode (LED) array. The experimental system is built based on a traditional bright field microscope, with the light source replaced by a programmable LED array, which provides angle-variable quasi-monochromatic illumination with an angular coverage of ±37 degrees in both x and y directions (corresponding to an illumination numerical aperture of ∼0.6). Transport of intensity equation (TIE) is utilized to recover the phase at different illumination angles, and the refractive index distribution is reconstructed based on the ODT framework under first Rytov approximation. The missing-cone problem in ODT is addressed by using the iterative non-negative constraint algorithm, and the misalignment of the LED array is further numerically corrected to improve the accuracy of refractive index quantification. Experiments on polystyrene beads and thick biological specimens show that the proposed approach allows accurate refractive index reconstruction while greatly reduced the system complexity and environmental sensitivity compared to conventional interferometric ODT approaches.     

An accurate gradient and Hessian reconstruction method for cell‐centered finite volume discretizations on general unstructured grids

In this paper, a novel reconstruction of the gradient and Hessian tensors on an arbitrary unstructured grid, developed for implementation in a cell‐centered finite volume framework, is presented. The reconstruction, based on the application of Gauss' theorem, provides a fully second‐order accurate estimate of the gradient, along with a first‐order estimate of the Hessian tensor. The reconstruction is implemented through the construction of coefficient matrices for the gradient components and independent components of the Hessian tensor, resulting in a linear system for the gradient and Hessian fields, which may be solved to an arbitrary precision by employing one of the many methods available for the efficient inversion of large sparse matrices. Numerical experiments are conducted to demonstrate the accuracy, robustness, and computational efficiency of the reconstruction by comparison with other common methods. Copyright © 2009 John Wiley & Sons, Ltd.     

荧光相位成像的光束扫描法

利用计算机控制振镜进行光束扫描，用锁相放大器进行增益调制与相位调节，最后再用计算机重建图像，实现钛宝石和红宝石的相位成像。分别完成了激发光和荧乐相移为π／１２、π／１４和７π／１２的成像，分析了系统的时间分辨率和空间分辨率，提出了实用化发展的方向。     

Non-interactive geometric probing: Reconstructing non-convex polygons

We address the problem of characterizing polygonal shapes that can be reconstructed from a class of scanners that have asymmetric resolution. We approach this problem using the methodology of non-interactive probing.

Laser raster scanners provide very high precision along the direction of a scan, but it is not practical to place scans very close to each other. A system capable of generating an omni-directional scan pattern can make a series of directional measurements sufficient to permit the reconstruction of a scanned polygon based on the position of edge crossings and the path of the scanning beam between edge crossings. We provide a procedure to reconstruct a polygon from such a data set, as well as a characterization of the shapes that can be reconstructed given a particular scan density. Our system applies to both concave and convex polygons, as well as to polygons containing holes.     

Observation of Electrostatic Microfield Inside Charged Latex Particles by Digital Reconstruction from Electron Holograms

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