SUMMARY Due to the influence of variations in landform, geophysical data acquisition is usually sub-sampled. Reconstruction of the seismic wavefield from sub-sampled data is an ill-posed inverse problem. Compressive sensing can be used to recover the original geophysical data from the sub-sampled data. In this paper, we consider the wavefield reconstruction problem as a com-pressive sensing and...

A problem of first-order bandpass sampling is that the indifferent disposition of the baseband spectrum may cause inconvenience in practical applications. To overcome it, we modify the first-order bandpass sampling theory according to the spectral arrangement of the sampled signal. We consider two situations on the arrangement of the shifted replicas of the bandpass signal spectrum: the normal ...

Data which are sampled more densely than the Nyquist limit in k-space are weighted prior to reconstruction by the inverse of the local sampling density. This work considers the effects of weighting data that are sampled less densely than the Nyquist limit. It specifically analyzes azimuthally undersampled projection reconstruction, variable density spirals, and variable density phase encoding. ...

We consider the approximate solution of linear ill-posed inverse problems of high dimension with a simulation-based algorithm that approximates the solution within a low-dimensional subspace. The algorithm uses Tikhonov regularization, regression, and low-dimensional linear algebra calculations and storage. For sampling efficiency, we use variance reduction/importance sampling schemes, speciall...

Sequential estimation of a probability p by means of inverse binomial sampling is considered. For μ1, μ2 > 1 given, the accuracy of an estimator p̂ is measured by the confidence level Pr[p/μ2 ≤ p̂ ≤ pμ1]. The confidence levels c0 that can be guaranteed for p unknown, i.e. such that Pr[p/μ2 ≤ p̂ ≤ pμ1] ≥ c0 for all p ∈ (0, 1), are investigated. It is shown that, within the general class of randomiz...

Abstract We consider the direct and inverse scattering problems for partially coated obstacles. To this end, we first use the method of integral equations of the first kind together with variational methods to solve a scattering problem for the Helmholtz equation where the scattered field satisfies mixed Dirichletimpedance boundary conditions on the Lipschitz boundary of the scatterer D. We the...

As a rule of thumb, sampling methods for inverse scattering problems suffer from interior eigenvalues of the obstacle. Indeed, throughout the history of such algorithms one meets the phenomenon that if the wave number meets some resonance frequency of the scatterer, then those methods can only be shown to work under suitable modifications. Such modifications often require a-priori knowledge, co...