Related papers: Stabilizing Inverse Problems by Internal Data
Ultrasound modulated optical tomography, also called acousto-optics tomography, is a hybrid imaging modality that aims to combine the high contrast of optical waves with the high resolution of ultrasound. We follow the model of the…
We study the inverse problem of deducing the dynamical characteristics (such as the potential field) of large systems from kinematic observations. We show that, for a class of steady-state systems, the solution is unique even with…
In real-world problems, environmental noise is often idealized as Gaussian white noise, despite potential temporal dependencies. The Linear Inverse Model (LIM) is a class of data-driven methods that extract dynamic and stochastic…
Most existing learning-based methods for solving imaging inverse problems can be roughly divided into two classes: iterative algorithms, such as plug-and-play and diffusion methods leveraging pretrained denoisers, and unrolled architectures…
Thermally bistable fluid tends to self-organize into clouds of hot and cold material, which are internally uniform and separated by thin conduction fronts. The evolution of these clouds has been studied for isobaric systems, but when…
In recent years, discriminative self-supervised methods have made significant strides in advancing various visual tasks. The central idea of learning a data encoder that is robust to data distortions/augmentations is straightforward yet…
Transitive consistency is an intrinsic property for collections of linear invertible transformations between Euclidean coordinate frames. In practice, when the transformations are estimated from data, this property is lacking. This work…
This report addresses the boundary value problem for a second-order linear singularly perturbed FIDE. Traditional methods for solving these equations often face stability issues when dealing with small perturbation parameters. We propose an…
Many industrial machine learning (ML) systems require frequent retraining to keep up-to-date with constantly changing data. This retraining exacerbates a large challenge facing ML systems today: model training is unstable, i.e., small…
In this paper we prove a stable determination of the coefficients of the time-harmonic Maxwell equations from local boundary data. The argument --due to Isakov-- requires some restrictions on the domain.
Stability enforcement remains a challenge in data-driven control paradigms, where no parametrised model of the system is available. For instance, the system's instabilities can be estimated in order to enforce a closed-loop stability…
Conditional stability estimates allow us to characterize the degree of ill-posedness of many inverse problems, but without further assumptions they are not sufficient for the stable solution in the presence of data perturbations. We here…
The attenuation of ultrasound waves in photoacoustic and thermoacoustic imaging presents an important drawback in the applicability of these modalities. This issue has been addressed previously in the applied and theoretical literature, and…
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…
Inverse Dynamics Models (IDMs) map visual observations to low-level action commands, serving as central components for data labeling and policy execution in embodied AI. However, their performance degrades severely under manipulator…
We present iDARR, a scalable iterative Data-Adaptive RKHS Regularization method, for solving ill-posed linear inverse problems. The method searches for solutions in subspaces where the true solution can be identified, with the data-adaptive…
This paper presents a novel strategy for high-fidelity image restoration by characterizing both local smoothness and nonlocal self-similarity of natural images in a unified statistical manner. The main contributions are three-folds. First,…
In the present work, we demonstrate how the pseudoinverse concept from linear algebra can be used to represent and analyze the boundary conditions of linear systems of partial differential equations. This approach has theoretical and…
Hybrid inverse problems such as Acousto-Electric Tomography, Current Density Imaging or Magnetic Resonance Electric Impedance Tomography are concerned with reconstructing the electrical conductivity from interior measurements. For a…
The main features of the statistical approach to inverse problems are described on the example of a linear model with additive noise. The approach does not use any Bayesian hypothesis regarding an unknown object; instead, the standard…