Related papers: Optimal Space-Variant Anisotropic Tikhonov Regular…
Proper regularization is crucial in inverse problems to achieve high-quality reconstruction, even with an ill-conditioned measurement system. This is particularly true for three-dimensional photoacoustic tomography, which is computationally…
This paper presents a novel numerical method for the Newton seismic full-waveform inversion (FWI). The method is based on the full-space approach, where the state, adjoint state, and control variables are optimized simultaneously. Each…
In this paper, we study the performance of Full Waveform Inversion (FWI) from time-harmonic Cauchy data via conditional well-posedness driven iterative regularization. The Cauchy data can be obtained with dual sensors measuring the pressure…
Regularization plays a pivotal role in ill-posed machine learning and inverse problems. However, the fundamental comparative analysis of various regularization norms remains open. We establish a small noise analysis framework to assess the…
In this work, we propose a high-order regularization method to solve the ill-conditioned problems in robot localization. Numerical solutions to robot localization problems are often unstable when the problems are ill-conditioned. A typical…
Solving inverse problems involving measurement noise and modeling errors requires regularization in order to avoid data overfit. Geophysical inverse problems, in which the Earth's highly heterogeneous structure is unknown, present a…
The problem of numerical differentiation can be thought of as an inverse problem by considering it as solving a Volterra equation. It is well known that such inverse integral problems are ill-posed and one requires regularization methods to…
Inverse problems and regularization theory is a central theme in contemporary signal processing, where the goal is to reconstruct an unknown signal from partial indirect, and possibly noisy, measurements of it. A now standard method for…
Pre-trained vision foundation models (VFMs) provide strong semantic representations, yet their patch-level features are inherently coarse, limiting their effectiveness on tasks requiring fine-grained localization, dense prediction, and…
This paper investigates unsupervised learning of Full-Waveform Inversion (FWI), which has been widely used in geophysics to estimate subsurface velocity maps from seismic data. This problem is mathematically formulated by a second order…
Many regression and classification procedures fit a parameterized function $f(x;w)$ of predictor variables $x$ to data $\{x_{i},y_{i}\}_1^N$ based on some loss criterion $L(y,f)$. Often, regularization is applied to improve accuracy by…
A number of regularization methods for discrete inverse problems consist in considering weighted versions of the usual least square solution. However, these so-called filter methods are generally restricted to monotonic transformations,…
Iterative inversion of seismic, ultrasonic, and other wave data by local gradient-based optimization of mean-square data prediction error (Full Waveform Inversion or FWI) can fail to converge to useful model estimates if started from an…
In this thesis, we offer a thorough investigation of different regularisation terms used in variational imaging problems, together with detailed optimisation processes of these problems. We begin by studying smooth problems and partially…
Full-waveform inversion (FWI) with extended sources first computes wavefields with data-driven source extensions, such that the simulated data in inaccurate velocity models match the observed counterpart well enough to prevent cycle…
Scarcity of hydrocarbon resources and high exploration risks motivate the development of high fidelity algorithms and computationally viable approaches to exploratory geophysics. Whereas early approaches considered least-squares…
In the process of tunnel excavation, advanced geological prediction technology has become indispensable for safe, economical, and efficient tunnel construction. Although traditional methods such as drilling and geological analysis are…
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…
In this paper we propose a new statistical stopping rule for constrained maximum likelihood iterative algorithms applied to ill-posed inverse problems. To this aim we extend the definition of Tikhonov regularization in a statistical…
To solve convex optimization problems with a noisy gradient input, we analyze the global behavior of subgradient-like flows under stochastic errors. The objective function is composite, being equal to the sum of two convex functions, one…