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Dissipative Wave Model Fitting Using Localized Sources

Frégnac, Yves; Peyré, Gabriel; Schmidt, Nicolas (2011), Dissipative Wave Model Fitting Using Localized Sources, 10th International Conference on Mathematical and Numerical Aspects of Waves (Waves 2011), 2011-07, Vancouver, Canada

Type
Communication / Conférence
External document link
http://hal.archives-ouvertes.fr/hal-00570685/fr/
Date
2011
Conference title
10th International Conference on Mathematical and Numerical Aspects of Waves (Waves 2011)
Conference date
2011-07
Conference city
Vancouver
Conference country
Canada
Pages
4
Metadata
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Author(s)
Frégnac, Yves
Peyré, Gabriel
Schmidt, Nicolas cc
Abstract (EN)
This paper introduces a novel method to estimate the parameters of a linear dissipative wave model from noisy observations. We focus on the case of constant coefficients and an unknown localized source. These constraints are motivated by applications in computational neuroscience and in particular separation of sources in the visual cortex in optical imaging modality. The proposed method takes advantage of the specificity of the model, namely the small number of parameters and the knowledge of the spatial support of the sources. It makes use of a temporal dimensionality reduction performed using a Laplace transform to drastically reduce the numerical complexity of the method. A Green kernel representation of the partial differential equation (PDE) solution exploiting the locality of the sources allows us to recover the parameters without the precise knowledge of the sources. A numerical evaluation of the method on synthetic data shows the strong robustness to noise of our method.
Subjects / Keywords
Green functions; Partial differential equations; Propagation; Inverse problems

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