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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Inverse Problems and Their Applications
逆问题 系统辨识 正问题
2023/5/12
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...
Recovering Edges in Ill-Posed Inverse Problems:Optimality of Curvelet Frames
Ill-Posed Inverse Problems Regularization Singular Value Decomposition Radon Transform Deconvolution Edge Edge-Preserving Regularization Wavelets Curvelets Ridgelets Wavelet-Vaguelette-Decomposition Wavelet Shrinkage Minimax Estimation Optimal Rates of Convergence White Noise Model
2015/6/17
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 us...
A New Global Stochastic Search Approach for Inverse Problems: Application to Ultrasound Modulated Optical Tomography
inverse problems global stochastic search discretized Kushner-Stratonovich equation gain-based update ultrasound modulated optical tomography
2013/6/14
A global stochastic search method, which is strictly derivative-free yet directed through a gain-based additive update term, is proposed and applied to the inverse problem of ultrasound modulated opti...
Practical Tikhonov Regularized Estimators in Reproducing Kernel Hilbert Spaces for Statistical Inverse Problems
Tikhonov Regularized Estimators Reproducing Kernel Hilbert Spaces Statistical Inverse Problems
2013/6/13
Regularized kernel methods such as support vector machines (SVM) and support vector regression (SVR) constitute a broad and flexible class of methods which are theoretically well investigated and comm...
Efficient Estimators for Sequential and Resolution-Limited Inverse Problems
deconvolution ill-posed image processing sig-nal recovery
2012/9/18
A common problem in the sciences is that a signal of interest is observed only indirectly, through smooth functionals of the signal whose values are then obscured by noise. In suchinverse problems, th...
Besov priors for Bayesian inverse problems
Bayesian inverse problems Fernique-like theorem
2011/6/16
We consider the inverse problem of estimating a function u from
noisy, possibly nonlinear, observations. We adopt a Bayesian approach to the
problem and widen the existing theory, which is developed...
A Threshold Regularization Method for Inverse Problems
Inverse problems regularization oracle inequalities hard thresholding
2011/6/16
A number of regularization methods for discrete inverse problems consist in considering weighted versions of the usual least square solution. However, these so-called filter methods are generally res...
The Convex Geometry of Linear Inverse Problems
Optimization and Control (math.OC) Statistics Theory (math.ST)
2010/12/17
In applications throughout science and engineering one is often faced with the challenge of solving an ill-posed inverse problem, where the number of available measurements is smaller than the dimensi...
Empirical risk minimization in inverse problems
Deconvolution empirical risk minimization multivariate density estimation nonparametric function estimation Radon transform tomography
2010/3/9
We study estimation of a multivariate function f :Rd
!R when
the observations are available from the function Af, where A is a
known linear operator. Both the Gaussian white noise model and
densit...
Minimax Signal Detection in Ill-Posed Inverse Problems
Minimax Signal Detection Ill-Posed Inverse Problems
2010/3/9
We consider the signal detection problem for mildly, severely and extremely
ill-posed inverse problems with Sobolev, analytic and generalized analytic classes
of functions under the Gaussian white n...
Importance Re-sampling MCMC for Cross-Validation in Inverse Problems
Cross-validation Inverse Importance Re-sampling Model fit Re-use
2009/9/22
This paper presents a methodology for cross-validation in the context of Bayesian
modelling of situations we loosely refer to as iverse problems It is motivated by
an example from palaeoclimatology ...
Needlet algorithms for estimation in inverse problems
statistical inverse problems minimax estimation second-generation wavelets
2009/9/16
We provide a new algorithm for the treatment of inverse problems which combines the traditional SVD inversion with an appropriate thresholding technique in a well chosen new basis. Our goal is to devi...
Adaptive complexity regularization for linear inverse problems
Inverse Problems Adaptive Estimation Regularization
2009/9/16
We tackle the problem of building adaptive estimation procedures for ill-posed inverse problems. For general regularization methods depending on tuning parameters, we construct a penalized method that...
Quadratic functional estimation in inverse problems
Gaussian sequence model inverse problem minimax upper bounds parametric rate Pinsker estimator projection estimator
2010/3/18
We consider in this paper a Gaussian sequence model of observations Yi, i ≥ 1
having mean (or signal) θi and variance σi which is growing polynomially like i
,γ > 0. This model describes a large pan...
Needlet algorithms for estimation in inverse problems
statistical inverse problems minimax estimation second-generation wavelets
2010/4/29
We provide a new algorithm for the treatment of inverse problems
which combines the traditional SVD inversion with an appropriate
thresholding technique in a well chosen new basis. Our goal is to de...