A framework to perform high-order deconvolution for finite-volume method on simplicial meshes

In this article, a new framework to design high-order approximations in the context of node-centered finite volumes on simplicial meshes is proposed. The major novelty of this method is that it relies on very simple and compact differential operators, which is a critical point to achieve good performances in the High-performance computing context. This method is based on deconvolution between nodal and volume-average values, which can be conducted to any order. The interest of the new method is illustrated through three different applications: mesh-to-mesh interpolation, levelset curvature computation, and numerical scheme for convection. Higher order can also be achieved within the present framework by introducing high-rank tensors. Although these tensors feature much symmetries, their manipulation can quickly become an overwhelming task. For this reason and without loss of generality, the present articles are limited to third-order expansion. This method, although tightly connected to the k-exact schemes theory, does not rely on successive corrections: the high-order property is obtained in a single operation, which makes them more attractive in terms of performances.     

基于迁移学习的原子力显微镜成像恢复方法

受限于探针针尖结构尺寸,用原子力显微镜进行微纳测量时会产生图像边缘失真.提出了一种基于迁移学习的原子力显微镜成像恢复方法,通过迁移学习训练源模型和靶模型实现一维栅格成像恢复.该方法采用数学形态法中的腐蚀算法生成栅格点云数据,通过U-Net网络源模型从点云中提取针尖卷积效应的特征向量,将权重参数迁移至U-Net网络靶模型,靶模型在自适应正则化方法下进行监督学习.实验结果表明,该方法能有效恢复一维栅格的原子力显微镜测量图像,提高横向分辨力,可用于纳米栅格的线宽检测上.     

一种基于序贯估计的直达声区水面舰船 被动测距方法 *

该文利用基于射线的盲解卷积方法，从直达声区的水面舰船噪声中提取出船和锚系于海底的垂直接收阵之间的时域信道响应，并利用直达波在不同阵元相对于参考阵元的到达时间差，通过序贯方法，利用射线模型和声速剖面信息，对水面舰船距接收阵的距离进行了估计。通过处理海深约为580 m的2016年美国圣巴巴拉海峡的实验数据，对1.6~3.5 km直达声区范围内Anna Maersk商船与垂直阵之间的距离进行了估计，验证了测距方法的有效性，并将结果与系统测量值和几何方法的估计值进行了比较。由于该方法不需要对海底参数进行估计，所以在海底参数未知时要优于传统匹配场方法；在声速剖面存在跃层且海底为多层分布的复杂信道条件下，该方法仍能对距离进行有效估计，且与测量值的相对误差在6%以内，小于几何方法的估计误差，测距结果精度较高。     

A mathematical and physical Study of multiscale deconvolution models of turbulence

This work presents a rigorous analysis of mathematical and physical properties for solutions of multiscale deconvolution turbulence models. We show that solutions of these models exactly conserve model quantities for the integral invariants of fundamental physical importance: kinetic energy, helicity, and (in two dimensions) enstrophy. The kinetic energy conservation is the key that allows us to next apply the phenomenology of homogeneous, isotropic turbulence to establish the existence of a model energy cascade and, in particular, that the cascade exhibits enhanced energy dissipation in a secondary accelerated cascade, which ends at the model's microscale (which we establish is larger than the Kolmogorov microscale). We also prove that the model dissipates energy at the same rate as true turbulent flow, ～ O(U³ ∕ L), independent of Reynolds number. Lastly, we prove the existence of global attractors for the model solutions; the proof of which also shows that solutions are actually one degree of regularity higher than previously known. Copyright © 2012 John Wiley & Sons, Ltd.     

Experimental shift allowance in the deconvolution of SIMS depth profiles

We study the deconvolution of the secondary ion mass spectrometry (SIMS) depth profiles of silicon and gallium arsenide structures with doped thin layers. Special attention is paid to allowance for the instrumental shift of experimental SIMS depth profiles. This effect is taken into account by using Hofmann's mixing‐roughness‐information depth model to determine the depth resolution function. The ill‐posed inverse problem is solved in the Fourier space using the Tikhonov regularization method. The proposed deconvolution algorithm has been tested on various simulated and real structures. It is shown that the algorithm can improve the SIMS depth profiling relevancy and depth resolution. The implemented shift allowance method avoids significant systematic errors of determination of the near‐surface delta‐doped layer position. Copyright © 2013 John Wiley & Sons, Ltd.     

A defect correction approach to turbulence modeling

A method for resolving turbulent flow problems is presented, aiming at competing with the existing mathematical tractable Approximate Deconvolution Models in terms of accuracy, and outperforming these models in terms of the computational time needed. Full numerical analysis is performed, and the method is shown to be stable, easy to implement and parallelize, and computationally fast. The proposed method employs the defect correction approach to solve spatially filtered Navier–Stokes equations. A simple numerical test is provided that compares the method against the approximate deconvolution turbulence model (ADM). When resolving a fluid flow at high Reynolds number, the numerical example verifies the key feature of the method: while having the accuracy comparable to that of the ADM, the method computes in less than 80% of the time needed for the turbulence model—even before the parallelization.© 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 268–288, 2015     

Spectral analysis of Sr 3d XPS spectrum in Sr-containing hydroxyapatite

The Sr 3d X-ray photoelectron spectroscopy (XPS) spectrum of Sr-containing hydroxyapatite (SHAp) overlaps completely with the P 2p spectrum. Thus, the chemical state identification of Sr in SHAp is a challenging task. In this work, the Sr 3d spectrum was isolated from the overlapping spectra for analyzing the chemical state of Sr using a generic peak-fitting method. The SHAp layers containing various Sr concentrations were produced on a Ti substrate using a chemical treatment process with a calcium phosphate slurry that included Sr (NO₃)₂. The distribution of the constituent elements changed according to the Sr concentration, implying that the chemical state of Sr varied with concentration. The isolation of the Sr 3d XPS spectrum was conducted via spectral deconvolution using the P 2p spectrum corresponding to HAp. The isolated Sr 3d spectrum revealed that the chemical state of Sr was in SrO and Sr-substituted HAp states, and their ratio varied with the Sr concentration in the layer. The SrO to Sr-substituted HAp ratios affected the Sr ion releasing behavior from the SHAp layer, supporting the validity of the obtained analytical results.     

A piecewise local regularized Richardson-Lucy algorithm for remote sensing image deconvolution

As it is not possible to obtain an accurate point spread function (PSF) in remote sensing imaging, classic deconvolution methods such as Wiener filtering often introduce strong noise and ringing artifacts, which contaminate the restored images. In this paper, we modify the standard Richarson-Lucy (RL) algorithm with a piecewise local regularization term and combine it with residual deconvolution method. Experimental results show that it is effective in suppressing negative effects, and images with rich details and sharp edges are obtained.     

基于盲解卷积的水声信号恢复技术

信号在环境复杂多途严重的水声波导中传输后,接收到的信号时间长度被拉长,信号是失真的。在许多实际应用中,常常希望从已失真的接收信号中把原始信号波形恢复出来。本文利用盲解卷积技术对水声信号恢复进行研究。理论推演表明,在垂直阵条件下用人造的格林函数可成功地代替水声信道真实的格林函数,可以把非线性关系化解为线性关系,从而推导出依靠基阵记录下的信息去确定声源宽带信号原始波形和环境传播特征的公式和步骤。声场数值计算对6种海底类型进行,恢复后的宽带信号与原始信号的归一化相关系数均大于0.945,对硬海底多途严重的情况,收效特别明显,证明该方法的有效性。在青岛海试中恢复后信号的相关系数平均值为0.933,在青岛海试中利用这种解卷积技术去恢复信号是成功的。     

Best Fourier Approximation and Application in Efficient Blurred Signal Reconstruction

We expand upon the known results on sharp linear Fourier methods of approximation where the approximation is the best in terms of both rate and constant among all polynomial procedures of approximation. So far these results have been studied due to their mathematical beauty rather than their practical importance. In this paper we show that they are the core mathematics underlying best statistical methods of solving noisy ill-posed problems. In particular, we suggest a procedure for recovery of noisy blurred signals based on samples of small sizes where a traditional statistics concludes that the complexity of such a setting makes the problem not worthy of a further study. Thus, we present a problem where a combination of the classical approximation theory and statistics leads to interesting practical results.