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.