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This course will give an introduction to inverse problems for elliptic partial differential equations. The most famous example of such problems is the Calderón problem, which arises in seismic and med...
This course will give an introduction to inverse problems for elliptic partial differential equations. The most famous example of such problems is the Calderón problem, which arises in seismic and med...
The talk proposes a deep learning method specifically dealing with the forward and inverse problem of variable coefficient partial differential equations-Variable Coefficient Physics-Informed Neural N...
反问题和正问题是成对出现的。通常,学术界将已知原因(输入)、过程(模型)而探求结果(输出)的一类问题称为正问题。与此相对应,就有了两种反问题:已知模型、输出求未知输入的“溯源”问题和已知输入、输出来反求模型(或模型参数)的系统辨识问题。在现实社会和人类生活中,反问题无处不在;在关系国家命脉的经济生产和国防军事领域中反问题更是随处可见。例如,与人类健康福祉密切相关的无痛无损伤、在体表进行测量的医学诊...
磁共振成像是目前医学成像技术中功能最强大,技术门槛最复杂的技术之一。然而,相对其他成像模态较为缓慢的采集速度(较长的扫描时间)制约了磁共振成像在临床上的广泛应用。借助采样样本的数量与扫描时间的正比关系,通过减少采集的数据量(稀疏采样)来缩短磁共振采集时间是磁共振成像领域的重要途径,而从高度欠采样的数据中重建出高质量的图像可以近似为一个病态反问题,对这一问题的求解是快速磁共振成像领域的研究热点。本次...
Stochastic wave equations describe wave motion in random environments that is common in realistic situations. In this talk, I will present our recent studies on the inverse source and potential proble...
In this talk, recent progress on inverse problems for piezoelectric equations is discussed. We show a uniqueness result on recovering coefficients of piecewise homogeneous piezoelectric equations from...
Since its first proposal in 2018, deep image prior has emerged as a very powerful unsupervised deep learning technique for solving inverse problems. The approach has demonstrated very encouraging empi...
The summer school aims to introduce graduate students to the mathematical and computational aspects of inverse problems, particularly modern developments that emphasize the quantification of uncertain...
An inverse problem in science is the process of calculating from a set of observation data the causal factors (model parameters) that have produced them. It is called an inverse problem because it sta...
Inverse problems arise from the need to interpret indirect measurements. Such situations are common in many application areas such as medical imaging, nondestructive testing, underground prospecting, ...
We consider a model problem of recovering a function f(x1; x2) from noisy Radon data. The function f to be recovered is assumed smooth apart from a discontinuity along a C2 curve { i.e. an edge. We ...
Johnstone and Silverman (1997) described a level-dependent thresholding method for extracting signals from correlated noise. The thresholds were chosen to minimize a data based unbiased risk criteri...
Wave propagation in complex media is an ubiquitous phenomenon–applications include light propagation through the atmosphere, underwater acoustic, tomography, and innumerable other ones. These problems...
Addressing a variety of questions within Earth science disciplines entails the inference of the spatiotemporal distribution of parameters of interest based on observations of related quantities. Such ...

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