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Onétudie des estimations semiclassiques sur la résolvente d'opérateurs qui ne sont ni ellip-tiques ni autoadjoints, que l'on utilise pourétudier leprobì eme de Cauchy. En particulier on obtient une description précise du spectre pres de l'axe imaginaire, et des estimations de résolventè a l'intérieur du pseudo-spectre. On applique ensuite les résultatsà(More)
A nonlinear singularity-preserving solution to seismic image recovery with sparseness and continuity constraints is proposed. We observe that curvelets, as a directional frame expansion, lead to sparsity of seismic images and exhibit invariance under the normal operator of the linearized imaging problem. Based on this observation we derive a method for(More)
In this paper we use methods from partial differential equations, in particular microlo-cal analysis and theory of Fourier integral operators, to study seismic imaging in the wave-equation approach. Seismic data are commonly modeled by a high-frequency single scattering approximation. This amounts to a linearization in the medium coefficient about a smooth(More)
This paper provides a theoretical foundation for some common formulations of inverse problems in wave propagation, based on hyperbolic systems of linear integro-differential equations with bounded and measurable coefficients. The coefficients of these time-dependent partial differential equations respresent parametrically the spatially varying mechanical(More)
In this paper, we revisit the reverse-time imaging procedure. We discuss an inverse scattering transform derived from reverse-time migration (RTM), and establish its relation with generalized Radon transform inversion. In the process, the explicit evaluation of the so-called normal operator is avoided, at the cost of introducing other pseudodifferential(More)