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We present a Bayesian filtering approach for automatic estimation of dynamical source models from magnetoencephalographic data. We apply multi-target Bayesian filtering and the theory of Random Finite Sets in an algorithm that recovers the life times, locations and strengths of a set of dipolar sources. The reconstructed dipoles are clustered in time and(More)
In this letter, we investigate the impact of choosing different loss functions from the viewpoint of statistical learning theory. We introduce a convexity assumption, which is met by all loss functions commonly used in the literature, and study how the bound on the estimation error changes with the loss. We also derive a general result on the minimizer of(More)
Two psychophysics experiments are described, pointing out the significant role played by stochastic resonance in recognition of capital stylized noisy letters by the human perceptive apparatus. The first experiment shows that an optimal noise level exists at which the letter is recognized for a minimum threshold contrast. A simple two-parameter model that(More)
In regularized kernel methods, the solution of a learning problem is found by minimizing func-tionals consisting of the sum of a data and a complexity term. In this paper we investigate some properties of a more general form of the above functionals in which the data term corresponds to the expected risk. First, we prove a quantitative version of the(More)
The linear sampling method is a qualitative procedure for the visualization of both impenetrable and inhomogeneous scatterers, which requires the regularized solution of a linear ill-posed integral equation of the first kind. An open issue in this technique is the one of determining the optimal scatterer profile from the visualization maps in an automatic(More)
Automatic estimation of current dipoles from biomagnetic data is still a problematic task. This is due not only to the ill-posedness of the inverse problem but also to two intrinsic difficulties introduced by the dipolar model: the unknown number of sources and the nonlinear relationship between the source locations and the data. Recently, we have developed(More)
This paper proposes a qualitative approach to the inverse scattering problem of microwave tomography for breast cancer detection. In a 2D framework, the tumor inside the breast is regarded as an unknown scatterer placed inside an inhomogeneous and lossy background, formed by skin and fat. We firstly present in detail the mathematical formulation of the(More)
Chirp-pulse microwave computerized tomography (CP-MCT) is an imaging modality developed at the Department of Biocybernetics, University of Niigata (Niigata, Japan), which intends to reduce the microwave-tomography problem to an X-ray-like situation. We have recently shown that data acquisition in CP-MCT can be described in terms of a linear model derived(More)
A two-step reconstruction scheme is introduced to solve fixed frequency inverse scattering problems in Born approximation conditions. The aim of the approach is to achieve super-resolution effects by constraining the inversion method to exploit some a priori knowledge on the scatterer. Therefore, the first step is to apply the linear sampling method to the(More)