Related papers: On a Constrained Pseudoinverse for the Electromagn…
The subject of this thesis is in the area of Applied Mathematics known as Inverse Problems. Inverse problems are those where a set of measured data is analysed in order to get as much information as possible on a model which is assumed to…
Inverse problems, where in broad sense the task is to learn from the noisy response about some unknown function, usually represented as the argument of some known functional form, has received wide attention in the general scientific…
Inverse optimization refers to the inference of unknown parameters of an optimization problem based on knowledge of its optimal solutions. This paper considers inverse optimization in the setting where measurements of the optimal solutions…
Motivated by inverse problems with a single passive measurement, we introduce and analyze a new class of inverse spectral problems on closed Riemannian manifolds. Specifically, we establish two general uniqueness results for the recovery of…
In this work, we describe a new data-driven approach for inverse problems that exploits technologies from machine learning, in particular autoencoder network structures. We consider a paired autoencoder framework, where two autoencoders are…
We study a new family of inverse problems for recovering representations of corrupted data. We assume access to a pre-trained representation learning network R(x) that operates on clean images, like CLIP. The problem is to recover the…
We introduce in this document a direct method allowing to solve numerically inverse type problems for linear hyperbolic equations. We first consider the reconstruction of the full solution of the wave equation posed in $\Omega\times (0,T)$…
Diffusion models have emerged as powerful generative tools with applications in computer vision and scientific machine learning (SciML), where they have been used to solve large-scale probabilistic inverse problems. Traditionally, these…
There has recently been renewed recognition of the need to understand the consistency properties that must be preserved when a generalized matrix inverse is required. The most widely known generalized inverse, the Moore-Penrose…
Accurate solutions to inverse supersonic compressible flow problems are often required for designing specialized aerospace vehicles. In particular, we consider the problem where we have data available for density gradients from Schlieren…
Contrary to the traditional pursuit of research on nonuniform sampling of bandlimited signals, the objective of the present paper is not to find sampling conditions that permit perfect reconstruction, but to perform the best possible signal…
Inverse problems in statistical physics are motivated by the challenges of `big data' in different fields, in particular high-throughput experiments in biology. In inverse problems, the usual procedure of statistical physics needs to be…
We present the first framework to solve linear inverse problems leveraging pre-trained latent diffusion models. Previously proposed algorithms (such as DPS and DDRM) only apply to pixel-space diffusion models. We theoretically analyze our…
Electromagnetics has an important role to play in solving the next generation of geoscience problems. These problems are multidisciplinary, complex, and require collaboration. This is especially true at the base scientific level where the…
A simple inverse problem for the wave equation requires determination of both the wave velocity in a homogenous acoustic material and the transient waveform of an isotropic point radiator, given the time history of the wavefield at a remote…
The Gauss-Seidel method has been used for more than 100 years as the standard method for the solution of linear systems of equations under certain restrictions. This method, as well as Cramer and Jacobi, is widely used in education and…
The inverse potential problem consists in determining the density of the volume potential from measurements outside the sources. Its ill-posedness is due both to the non-uniqueness of the solution and to the instability of the solution with…
The support recovery problem consists of determining a sparse subset of a set of variables that is relevant in generating a set of observations, and arises in a diverse range of settings such as compressive sensing, and subset selection in…
In this paper, we are concerned with the inverse electromagnetic scattering problem of recovering a complex scatterer by the corresponding electric far-field data. The complex scatterer consists of an inhomogeneous medium and a possibly…
Inverse medium scattering problems arise in many applications, but in practice, the measurement data are often restricted to a limited aperture by physical or experimental constraints. Classical sampling methods, such as MUSIC and the…