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Descripción
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| Inverse problems are a special kind of optimization problems since the cost function involves observed data that is always affected by noise. This paper analyses the effect of noise in data and the effect of the regularization in the cost function topography for linear and nonlinear inverse problems. In the case of ill-conditioned inverse problems the noise in data is amplified back to the model parameters providing spurious solutions if no regularization techniques are used. Furthermore, the noise shifts the least squares solution of the linear system and deforms homogeneously the region of equivalence which is limited by a hyper-quadric surface. The zero-order Tikhonov?s regularization with a model of reference serves to limit the axes of hyper-quadric surface in the directions that span the kernel of the forward operator and to inform the model components of the solution that originally resided in the kernel. In the case of nonlinear inverse problems the effects are similar to the linear case, but the noise deforms the topography non-homogenously. The effect of the regularization in the linearized inverse problem is similar to the linear case, although it does not provoke the disappearance of the nonlinear equivalent models. Finally, the linearized and nonlinear uncertainty analyses generally provide very different risk assessment conclusions. | |
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Internacional
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Si |
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Nombre congreso
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4th Inverse Probems, Design and Optimization Symposium (IPDO 2013) |
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Tipo de participación
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960 |
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Lugar del congreso
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Albi, Francia |
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Revisores
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Si |
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ISBN o ISSN
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979-10-91526-01-2 |
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DOI
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Fecha inicio congreso
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26/06/2013 |
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Fecha fin congreso
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28/06/2013 |
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Desde la página
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1 |
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Hasta la página
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10 |
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Título de las actas
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Proceedings of the 4th Inverse Probems, Design and Optimization Symposium (IPDO 2013) |