The algorithms presented here are based on the recently developed theory of wavelets and are applicable to all Calderon-Zygmund and pseudo-differential operators, and indicate that many previously intractable problems become manageable with the techniques presented here.Expand

This paper treats the linearized inverse scattering problem for the case of variable background velocity and for an arbitrary configuration of sources and receivers. The linearized inverse scattering… Expand

This paper describes exact and explicit representations of the differential operators, ${{d^n } / {dx^n }}$, $n = 1,2, \cdots $, in orthonormal bases of compactly supported wavelets as well as the… Expand

An explicit approximation of the Fourier Transform of generalized functions of functions with singularities based on projecting such functions on a subspace of Multiresolution Analysis is obtained and a fast algorithm based on its evaluation is developed.Expand

It turns out that computing the exponential of strictly elliptic operators in the wavelet system of coordinates yields sparse matrices (for a finite but arbitrary accuracy) and this observation makes the approach practical in a number of applications.Expand

It is shown that the DRT can be used to compute various generalizations of the classical Radon transform (RT) and, in particular, the generalization where straight lines are replaced by curves and weight functions are introduced into the integrals along these curves.Expand

This paper further develops the separated representation by discussing the variety of mechanisms that allow it to be surprisingly efficient; addressing the issue of conditioning; and presenting algorithms for solving linear systems within this framework.Expand

A class of vector-space bases is introduced for the sparse representation of discretizations of integral operators possessing a smooth, nonoscillatory kernel possessing a finite number of singularities in each row or column as a sparse matrix, to high precision.Expand

We construct multiresolution representations of derivative and exponential operators with linear boundary conditions in multiwavelet bases and use them to develop a simple, adaptive scheme for the… Expand