Related papers: Seismic Tomography with Random Batch Gradient Reco…
We adopt the frozen Gaussian approximation (FGA) for modeling seismic waves. The method belongs to the category of ray-based beam methods. It decomposes seismic wavefield into a set of Gaussian functions and propagates these Gaussian…
Seismic tomography is a methodology to image the interior of solid or fluid media, and is often used to map properties in the subsurface of the Earth. In order to better interpret the resulting images it is important to assess imaging…
We propose the frozen Gaussian approximation for computation of high frequency wave propagation. This method approximates the solution to the wave equation by an integral representation. It provides a highly efficient computational tool…
In this paper, a stochastic algorithm for the efficient simulation and optimal control of networked wave equations based on the random batch method is proposed and analyzed. The random approximation is constructed by dividing the time…
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…
To obtain high-resolution images of subsurface structures from seismic data, seismic imaging techniques such as Full Waveform Inversion (FWI) serve as crucial tools. However, FWI involves solving a nonlinear and often non-unique inverse…
A challenge in high-dimensional inverse problems is developing iterative solvers to find the accurate solution of regularized optimization problems with low computational cost. An important example is computed tomography (CT) where both…
Stochastic gradient descent (SGD) holds as a classical method to build large scale machine learning models over big data. A stochastic gradient is typically calculated from a limited number of samples (known as mini-batch), so it…
We propose in this work RBM-SVGD, a stochastic version of Stein Variational Gradient Descent (SVGD) method for efficiently sampling from a given probability measure and thus useful for Bayesian inference. The method is to apply the Random…
Seismic imaging from sparsely acquired data faces challenges such as low image quality, discontinuities, and migration swing artifacts. Existing convolutional neural network (CNN)-based methods struggle with complex feature distributions…
In seismic waveform inversion, the reconstruction of the subsurface properties is usually carried out using approximative wave propagation models to ensure computational efficiency. The viscoelastic nature of the subsurface is often…
We study the Stochastic Gradient Descent (SGD) method in nonconvex optimization problems from the point of view of approximating diffusion processes. We prove rigorously that the diffusion process can approximate the SGD algorithm weakly…
We propose a new stochastic optimization framework for empirical risk minimization problems such as those that arise in machine learning. The traditional approaches, such as (mini-batch) stochastic gradient descent (SGD), utilize an…
Classical stochastic gradient methods for optimization rely on noisy gradient approximations that become progressively less accurate as iterates approach a solution. The large noise and small signal in the resulting gradients makes it…
Random projections or sketching are widely used in many algorithmic and learning contexts. Here we study the performance of iterative Hessian sketch for least-squares problems. By leveraging and extending recent results from random matrix…
We propose a new compressive imaging method for reconstructing 2D or 3D objects from their scattered wave-field measurements. Our method relies on a novel, nonlinear measurement model that can account for the multiple scattering phenomenon,…
Seismic waves are the most sensitive probe of the Earth's interior we have. With the dense data sets available in exploration, images of subsurface structures can be obtained through processes such as migration. Unfortunately, relating…
High-quality novel view synthesis for large-scale scenes presents a challenging dilemma in 3D computer vision. Existing methods typically partition large scenes into multiple regions, reconstruct a 3D representation using Gaussian splatting…
We propose a stochastic conditional gradient method (CGM) for minimizing convex finite-sum objectives formed as a sum of smooth and non-smooth terms. Existing CGM variants for this template either suffer from slow convergence rates, or…
This work focuses on developing and motivating a stochastic version of a wellknown inverse problem methodology. Specifically, we consider the iteratively regularized Gauss-Newton method, originally proposed by Bakushinskii for…