Related papers: Full Waveform Inversion using the Wasserstein metr…
Beamforming in plane-wave imaging (PWI) is an essential step in creating images with optimal quality. Adaptive methods estimate the apodization weights from echo traces acquired by several transducer elements. Herein, we formulate…
Wasserstein metrics are increasingly being used as similarity scores for images treated as discrete measures on a grid, yet their behavior under noise remains poorly understood. In this work, we consider the sensitivity of the signed…
Wasserstein gradient flow (WGF) is a common method to perform optimization over the space of probability measures. While WGF is guaranteed to converge to a first-order stationary point, for nonconvex functionals the converged solution does…
In recent years, uncertainty-aware full waveform inversion (FWI) has received increasing attention, with a growing emphasis on producing informative uncertainty estimates alongside inversion results. Bayesian inference methods--particularly…
Frequency-domain Full Waveform Inversion (FWI) is potentially amenable to efficient processing of full-azimuth long-offset stationary-recording seabed acquisition carried out with sparse layout of ocean bottom nodes (OBNs) and broadband…
Squared Wasserstein distance is a frequently used tool to measure discrepancy between probability distributions. This distance is typically computed between empirical measures of size $n$ from two underlying random samples. Unfortunately,…
We present a novel multiscale framework for analyzing sequences of probability measures in Wasserstein spaces over Euclidean domains. Exploiting the intrinsic geometry of optimal transport, we construct a multiscale transform applicable to…
Full-waveform inversion (FWI), a popular technique that promises high-resolution models, has helped in improving the salt definition in inverted velocity models. The success of the inversion relies heavily on having prior knowledge of the…
Full waveform inversion (FWI) plays an important role in velocity modeling due to its high-resolution advantages. However, its highly non-linear characteristic leads to numerous local minimums, which is known as the cycle-skipping problem.…
Seismic full waveform inversion (FWI) has seen promising advancements through deep learning. Existing approaches typically focus on task-specific models trained and evaluated in isolation that lead to limited generalization across different…
Full waveform inversion (FWI) is widely used in geophysics to reconstruct high-resolution velocity maps from seismic data. The recent success of data-driven FWI methods results in a rapidly increasing demand for open datasets to serve the…
This paper is devoted to theoretical and numerical investigation of the local minimum issue in seismic full waveform inversion (FWI). This paper provides a mathematical analysis of optimal transportation (OT) type objective function's…
Wasserstein Discriminant Analysis (WDA) is a new supervised method that can improve classification of high-dimensional data by computing a suitable linear map onto a lower dimensional subspace. Following the blueprint of classical Linear…
Nonnegative tensor factorization (NTF) has become an important tool for feature extraction and part-based representation with preserved intrinsic structure information from nonnegative high-order data. However, the original NTF methods…
Examining and interpreting of a large number of wireless endoscopic images from the gastrointestinal tract is a tiresome task for physicians. A practical solution is to automatically construct a two dimensional representation of the…
We present a semi-amortized variational inference framework designed for computationally feasible uncertainty quantification in 2D full-waveform inversion to explore the multimodal posterior distribution without dimensionality reduction.…
The quadratic Wasserstein metric has shown its power in measuring the difference between probability densities, which benefits optimization objective function with better convexity and is insensitive to data noise. Nevertheless, it is…
Full waveform inversion (FWI) can be expressed in a Bayesian framework, where the associated uncertainties are captured by the posterior probability distribution (PPD). In practice, solving Bayesian FWI with sampling-based methods such as…
Covariate shift arises when covariate distributions differ between source and target populations while the conditional distribution of the response remains invariant, and it underlies problems in missing data and causal inference. We…
Full Waveform Inversion can be made immune to cycle skipping by matching the recorded data arbitrarily well from inaccurate subsurface models. To achieve this goal, the simulated wavefields can be computed in an extended search space as the…