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High quality measurements are paramount to a successful application of experimental techniques in structural dynamics. The presence of noise and disturbances can significantly distort the information stored in the data and, if not…
Inverse analysis, such as model calibration, often suffers from a lack of informative data in complex real-world scenarios. The standard remedy, designing new experimental setups, is often costly and time-consuming, while readily available…
A new algorithm is developed to jointly recover a temporal sequence of images from noisy and under-sampled Fourier data. Specifically, we consider the case where each data set is missing vital information that prevents its (individual)…
Generative deep learning architectures can produce realistic, high-resolution fake imagery -- with potentially drastic societal implications. A key question in this context is: How easy is it to generate realistic imagery, in particular for…
We propose a data-assisted two-stage method for solving an inverse random source problem of the Helmholtz equation. In the first stage, the regularized Kaczmarz method is employed to generate initial approximations of the mean and variance…
Many data-driven decision problems are formulated using a nominal distribution estimated from historical data, while performance is ultimately determined by a deployment distribution that may be shifted, context-dependent, partially…
We introduce a data-driven approach to building reduced dynamical models through manifold learning; the reduced latent space is discovered using Diffusion Maps (a manifold learning technique) on time series data. A second round of Diffusion…
We show that the symmetries of image formation by scattering enable graph-theoretic manifold-embedding techniques to extract structural and timing information from simulated and experimental snapshots at extremely low signal. The approach…
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…
We investigate the identification of the time-dependent source term in the diffusion equation using boundary measurements. This facilitates tracing back the origins of environmental pollutants. Employing the concept of dynamic complex…
This thesis explores parameter estimation methods for rapidly reconstructing compact binary sources generating gravitational waves. It employs numerical linear algebra and meshfree approximation techniques to expedite waveform generation…
The phase retrieval problem asks to recover a natural signal $y_0 \in \mathbb{R}^n$ from $m$ quadratic observations, where $m$ is to be minimized. As is common in many imaging problems, natural signals are considered sparse with respect to…
Recent breakthroughs in synthetic data generation approaches made it possible to produce highly photorealistic images which are hardly distinguishable from real ones. Furthermore, synthetic generation pipelines have the potential to…
Recovering signals from low-order moments is a fundamental yet notoriously difficult task in inverse problems. This recovery process often reduces to solving ill-conditioned systems of polynomial equations. In this work, we propose a new…
Deep vision models are now mature enough to be integrated in industrial and possibly critical applications such as autonomous navigation. Yet, data collection and labeling to train such models requires too much efforts and costs for a…
Bayesian inference for high-dimensional inverse problems is computationally costly and requires selecting a suitable prior distribution. Amortized variational inference addresses these challenges via a neural network that approximates the…
This paper is concerned with a numerical method for a 3D coefficient inverse problem with phaseless scattering data. These are multi-frequency data generated by a single direction of the incident plane wave. Our numerical procedure consists…
The reflections caused by common semi-reflectors, such as glass windows, can impact the performance of computer vision algorithms. State-of-the-art methods can remove reflections on synthetic data and in controlled scenarios. However, they…
Diffusion generative models unlock new possibilities for inverse problems as they allow for the incorporation of strong empirical priors in scientific inference. Recently, diffusion models are repurposed for solving inverse problems using…
In micro-seismic event measurements, pinpointing the passive source's exact spatial and temporal location is paramount. This research advocates for the combined use of both P- and S-wave data, captured by geophone monitoring systems, to…