Related papers: Inversion of electromagnetic induction data using …
One fundamental problem when solving inverse problems is how to find regularization parameters. This article considers solving this problem using data-driven bilevel optimization, i.e. we consider the adaptive learning of the regularization…
We consider scattered data approximation in samplet coordinates with $\ell_1$-regularization. The application of an $\ell_1$-regularization term enforces sparsity of the coefficients with respect to the samplet basis. Samplets are…
The motivation of this work is an inverse problem for the acoustic wave equation, where an array of sensors probes an unknown medium with pulses and measures the scattered waves. The goal of the inversion is to determine from these…
Regularization plays a pivotal role in integrating prior information into inverse problems. While many deep learning methods have been proposed to solve inverse problems, determining where to apply regularization remains a crucial…
Electrolysis is crucial for eco-friendly hydrogen production, but gas bubbles generated during the process hinder reactions, reduce cell efficiency, and increase energy consumption. Additionally, these gas bubbles cause changes in the…
Electromagnetic induction methods are a common means for geophysical survey. For soil structures that are invariant in one spatial dimension such as trench structures, we propose a fast forward model based on a 2D response function, taking…
The semi-airborne transient electromagnetic method (SATEM) is capable of conducting rapid surveys over large-scale and hard-to-reach areas. However, the acquired signals are often contaminated by complex noise, which can compromise the…
This report extends our recent progress in tackling a challenging 3D inverse scattering problem governed by the Helmholtz equation. Our target application is to reconstruct dielectric constants, electric conductivities and shapes of front…
The inverse problem of electrical resistivity surveys (ERSs) is difficult because of its nonlinear and ill-posed nature. For this task, traditional linear inversion methods still face challenges such as suboptimal approximation and initial…
We introduce a novel algorithm for nonlinear processing of data gathered by an active array of sensors which probes a medium with pulses and measures the resulting waves. The algorithm is motivated by the application of array imaging. We…
The high complexity of various inverse problems poses a significant challenge to model-based reconstruction schemes, which in such situations often reach their limits. At the same time, we witness an exceptional success of data-based…
We study the problem of recovering the initial data of the two dimensional wave equation from values of its solution on the boundary $\partial \Om$ of a smooth convex bounded domain $\Om \subset \R^2$. As a main result we establish…
We present a study of the numerical solution of the two dimensional electrical impedance tomography problem, with noisy measurements of the Dirichlet to Neumann map. The inversion uses parametrizations of the conductivity on optimal grids.…
Waveform inversion is concerned with estimating a heterogeneous medium, modeled by variable coefficients of wave equations, using sources that emit probing signals and receivers that record the generated waves. It is an old and intensively…
Basement relief gravimetry is crucial in geophysics, especially for oil exploration and mineral prospecting. It involves solving an inverse problem to infer geological model parameters from observed data. The model represents basement…
Learning with limited data is one of the biggest problems of machine learning. Current approaches to this issue consist in learning general representations from huge amounts of data before fine-tuning the model on a small dataset of…
We propose a novel numerical inversion algorithm for the coefficients of parabolic partial differential equations, based on model reduction. The study is motivated by the application of controlled source electromagnetic exploration, where…
Extracting information from nonlinear measurements is a fundamental challenge in data analysis. In this work, we consider separable inverse problems, where the data are modeled as a linear combination of functions that depend nonlinearly on…
The Multiscale Fourier Transform of a seismic trace performs time-frequency analyses over a range of window lengths. The variation in window length captures local and global relative amplitudes between events, thereby allowing reflectivity…
Stably inverting a dynamic system model is the foundation of numerous servo designs. Existing inversion techniques have provided accurate model approximations that are often highly effective in feedforward controls. However, when the…