Related papers: WaRIance: wavefield reconstruction inversion with …
Stochastic partial differential equations have been used in a variety of contexts to model the evolution of uncertain dynamical systems. In recent years, their applications to geophysical fluid dynamics has increased massively. For a…
We provide a computationally and statistically efficient method for estimating the parameters of a stochastic covariance model observed on a regular spatial grid in any number of dimensions. Our proposed method, which we call the Debiased…
In this paper, we propose a stochastic method for solving equality constrained optimization problems that utilizes predictive variance reduction. Specifically, we develop a method based on the sequential quadratic programming paradigm that…
The state-of-the-art methods for estimating high-dimensional covariance matrices all shrink the eigenvalues of the sample covariance matrix towards a data-insensitive shrinkage target. The underlying shrinkage transformation is either…
In this work we investigate the practicality of stochastic gradient descent and recently introduced variants with variance-reduction techniques in imaging inverse problems. Such algorithms have been shown in the machine learning literature…
This paper investigates the shape reconstructions of sub-wavelength objects from near-field measurements in transverse electromagnetic scattering. This geometric inverse problem is notoriously ill-posed and challenging. We develop a novel…
We propose a variational regularization approach based on a multiscale representation called cylindrical shearlets aimed at dynamic imaging problems, especially dynamic tomography. The intuitive idea of our approach is to integrate a…
We propose and test a method to reduce the dimensionality of Full Waveform Inversion (FWI) inputs as computational cost mitigation approach. Given modern seismic acquisition systems, the data (as input for FWI) required for an…
Full-waveform inversion (FWI) is known as a seismic data processing method that achieves high-resolution imaging. In the inversion part of the method that brings high resolution in finding a convergence point in the model space, a local…
Variational approximation methods have proven to be useful for scaling Bayesian computations to large data sets and highly parametrized models. Applying variational methods involves solving an optimization problem, and recent research in…
Wavefront reconstruction in lateral shearing interferometry typically assumes that the shear amount is an integer multiple of the sampling interval. When the shear is fractional, approximating it with the nearest integer value leads to…
Geophysical models usually contain both sharp interfaces and smooth variations, and it is difficult to accurately account for both of these two types of medium parameter variations using conventional full-waveform inversion methods. In…
Seismic data are commonly modeled by a high-frequency single scattering approximation. This amounts to a linearization in the medium coefficient about a smooth background. The discontinuities are contained in the medium perturbation. The…
A tomographic technique called full-waveform inversion has recently shown promise as a fast, affordable, and safe modality to image the brain using ultrasound. However, its high computational cost and memory footprint currently limit its…
One of the goals in scaling sequential machine learning methods pertains to dealing with high-dimensional data spaces. A key related challenge is that many methods heavily depend on obtaining the inverse covariance matrix of the data. It is…
In this work, we derive a model for the covariance of the visual residuals in multi-view SfM, odometry and SLAM setups. The core of our approach is the formulation of the residual covariances as a combination of geometric and photometric…
Earthquakes cause lasting changes in static equilibrium, resulting in global deformation fields that can be observed. Consequently, deformation measurements such as those provided by satellite based InSAR monitoring can be used to infer an…
We introduce adaptive sampling methods for stochastic programs with deterministic constraints. First, we propose and analyze a variant of the stochastic projected gradient method where the sample size used to approximate the reduced…
Due to the irregular space-time sampling of sea surface observations, the reconstruction of sea surface dynamics is a challenging inverse problem. While satellite altimetry provides a direct observation of the sea surface height (SSH),…
Seismic full waveform inversion (FWI) is a powerful geophysical imaging technique that produces high-resolution subsurface models by iteratively minimizing the misfit between the simulated and observed seismograms. Unfortunately,…