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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...
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...
日前,根据IOP官方网站发布消息,东南大学数学系刘继军教授课题组2013年发表的两篇学术论文入选Inverse Problems 杂志2013年亮点论文。两篇论文中,课题组成员王丽艳的论文研究了图像处理中基于分数阶导数的新模型和算法,王海兵的论文研究了基于热传导模型的一类介质内部空腔的成像方法,皆具有重要的数学意义和广阔的工程应用前景。
We investigate the frequentist posterior contraction rate of nonparametric Bayesian procedures in linear inverse problems in both the mildly and severely ill-posed cases. A theorem is proved in a gene...
We study empirical and hierarchical Bayes approaches to the problem of estimating an infinite-dimensional parameter in mildly ill-posed inverse problems. We consider a class of prior distributions ind...

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