Inverse problems is a field of applied mathematics that finds wide application in both the scientific community and industry where the objective is to estimate some parameter of interest (PoI) from observations. These two quantities are related by a mapping known as the parameter-to-observable (PtO) map, which may be nonlinear. While the forward problem may be well-posed, the inverse problem is often ill-posed, making parameter estimation a difficult problem. Ill-posedness in the Hadamard sense means that at least one of the following is true: 1) the solution does not exist, 2) the solution is not unique, or 3) the solution does not depend continuously on the data. In cases of interest where the PtO map is an observational operator acting o...
Inverse problems involve extracting the internal structure of a physical system from noisy measureme...
My thesis presents several novel methods to facilitate solving large-scale inverse problems by utili...
Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Progra...
Paper I considers piecewise affine inverse problems. This is a large group of nonlinear inverse prob...
International audienceSparse data models are powerful tools for solving ill-posed inverse problems. ...
The Bayesian formulation for inverse problems gives a way of making inferences about unknown quantit...
Inverse problems – the process of recovering unknown parameters from indirect measurements – are enc...
Inverse problems arise in many applications in science and engineering. They are characterized by th...
The subject of inverse problems in differential equations is of enormous practical importance, and h...
Inverse problems are often ill posed, with solutions that depend sensitively on data. In any numeric...
This paper considers the problem of approximating the inverse of the wave-equation Hessian, also cal...
Obtaining slip distributions for earthquakes results in an ill-posed inverse problem. While this imp...
Parameter estimation has wide applications in such fields as finance, biological science, weather pr...
Abstract—Quantifying uncertainties in large-scale simulations has emerged as the central challenge f...
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Electrical Engineering and Comp...
Inverse problems involve extracting the internal structure of a physical system from noisy measureme...
My thesis presents several novel methods to facilitate solving large-scale inverse problems by utili...
Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Progra...
Paper I considers piecewise affine inverse problems. This is a large group of nonlinear inverse prob...
International audienceSparse data models are powerful tools for solving ill-posed inverse problems. ...
The Bayesian formulation for inverse problems gives a way of making inferences about unknown quantit...
Inverse problems – the process of recovering unknown parameters from indirect measurements – are enc...
Inverse problems arise in many applications in science and engineering. They are characterized by th...
The subject of inverse problems in differential equations is of enormous practical importance, and h...
Inverse problems are often ill posed, with solutions that depend sensitively on data. In any numeric...
This paper considers the problem of approximating the inverse of the wave-equation Hessian, also cal...
Obtaining slip distributions for earthquakes results in an ill-posed inverse problem. While this imp...
Parameter estimation has wide applications in such fields as finance, biological science, weather pr...
Abstract—Quantifying uncertainties in large-scale simulations has emerged as the central challenge f...
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Electrical Engineering and Comp...
Inverse problems involve extracting the internal structure of a physical system from noisy measureme...
My thesis presents several novel methods to facilitate solving large-scale inverse problems by utili...
Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Progra...