I approximate the inverse Hessian (L′L)−1, where L is a Born modeling operator and L′ is the corresponding adjoint RTM operator, with non-stationary matching filters. These non-stationary filters can be seen as a low-rank approximation of the true inverse Hessian. For 3D least-squares imaging, I use these matching filters to precondition the inversion of prestack seismic data and observe a sign...

We develop a theory of stratified $LM$-filters which generalizes the theory of stratified $L$-filters. Our stratification condition explicitly depends on a suitable mapping between the lattices $L$ and $M$. If $L$ and $M$ are identical and the mapping is the identity mapping, then we obtain the theory of stratified $L$-filters. Based on the stratified $LM$-filters, a general theory of lattice-v...

Introduction: The Problem • Many signals are not stationary of the second order (their Autocorrelation Function (ACF) is time-varying) • The ACF is used to develop filters and predictors (e.g. for signal compression) • This suggests that we need filters and predictors that are time-varying • A common approach has been to assume local stationarity: We can estimate filters for the signal by using...

I approximate the inverse Hessian (L′L)−1, where L is a Born modeling operator and L′ is the corresponding adjoint RTM operator, with non-stationary matching filters. These non-stationary filters can be seen as a low-rank approximation of the true inverse Hessian. For 3D least-squares imaging, I use these matching filters to precondition the inversion of prestack seismic data and observe a sign...

introduction one of the most important pre-processing steps in optical coherence tomography (oct) is reducing speckle noise, resulting from multiple scattering of tissues, which degrades the quality of oct images. materials and methods the present study focused on speckle noise reduction and edge detection techniques. statistical filters with different masks and noise variances were applied on ...

The ideal regularizer is the inverse of the model covariance matrix. Often the model covariance matrix has a complicated structure that is difficult to characterize. Non-stationary prediction error filters (PEF) have the ability to describe complicated model behavior. Non-stationary filters are effective regularizers for missing data and tomography problems.

Most of the commonly used stationary filtering techniques, performed either in the spatial or frequency domains, fail to produce good results for noisy signals with fast varying non-stationary structures. The filtering results could be improved by using space/spatial-frequency based non-stationary filters. Hence, a robust approach to space/spatial-frequency analysis of two-dimensional noisy sig...