arXiv subjects

Chrysoula Tsogka

Publications and source records attributed to Chrysoula Tsogka.

At least 19 recordsLinked to original sources

arXiv2026

Iterative Atom Refinement: A Monotonicity Principle for Dictionary Learning

Dictionary learning seeks to recover an unknown dictionary $A$ from observations ${\bf y}_i = A{\bf x}_i$ with sparse coefficient vectors ${\bf x}_i$. We introduce the \emph{Iterative Atom Refinement} (IAR) algorithm, a simple procedure for recovering individual dictionary atoms. Starting from a random direction, IAR repeatedly selects the observations most strongly correlated with the current iterate and updates the direction by averaging the selected data. Our main contribution is a rigorous convergence theory of IAR. Using high-dimensional probabilistic estimates and a novel monotonicity principle for atom-selection probabilities, we show that a small initial advantage of one atom is amplified until that atom is isolated. Under our model assumptions, IAR identifies a generating atom after only three refinement steps. Numerical experiments support the theory and show that the resulting dynamics accurately capture the behavior observed in dictionary refinement.

cs.LG↗

arXiv2026

Waves 2026 Book of Abstracts

WAVES 2026, 17th International Conference on Mathematical and Numerical Aspects of Wave Propagation Concordia University (John Molson Building), Montreal, Canada, June 22-26, 2026 WAVES 2026 is the seventeenth meeting in a long-running biennial series that has, throughout its history, alternated between Europe and North America to advance the mathematical and numerical study of wave propagation. Hosted at the John Molson Building of Concordia University in Montreal from June 22 to 26, 2026, the conference continues this tradition as a leading international forum where theory, computation, and application meet. The scientific program spans the full breadth of mathematical and numerical techniques for wave phenomena, from the modeling and analysis of the governing partial differential equations to the design, analysis, and implementation of efficient computational methods. Representative themes include acoustic, electromagnetic, elastic, and seismic wave propagation; scattering and inverse problems; high-frequency and asymptotic methods; finite element, boundary integral, and time-domain discretizations; and absorbing boundary conditions and domain truncation, with applications reaching across the physical sciences and engineering.

math.NA↗

arXiv2026

Solving forward and inverse wave scattering via boundary integral equations and deep learning. Applications to cloaking design

We propose a deep learning framework based on an encoder-decoder architecture for the design and evaluation of cloaking devices, demonstrated in this work for two-dimensional wave propagation governed by the Helmholtz equation. The cloaks under consideration are concentric layered media surrounding the object, whose geometry and material parameters determine the scattering response. We consider circular and object-fitted layer configurations and parameterize all designs by the layer thicknesses, enabling a unified representation for direct comparison of different cloaks for the same object. Training data are generated using a boundary element formulation suitable for geometries where analytic solutions are not available, and neural networks are trained with standard hyperparameters on geometry-specific datasets. The proposed approach is applied to circular, star-shaped, and kite-shaped objects. Results show that object-fitted configurations consistently outperform simpler circular-layer designs in scattering reduction, highlighting the importance of geometry in cloaking performance. Overall, we present a flexible, data-driven approach for systematic comparison of cloaking strategies, with potential extension to more complex geometries and broadband settings.

physics.comp-ph↗

arXiv2026

Discretization in Multilayered Media with High Contrasts: Is It All About the Boundaries?

Wave propagation in multilayered media with high material contrasts poses significant numerical challenges, as large variations in wavenumbers lead to strong reflections and complex transmission of the incoming wave field. To address these difficulties, we employ a boundary integral formulation thereby avoiding volumetric discretization. In this framework, the accuracy of the numerical solution depends strongly on how the material interfaces are discretized. In this work, we demonstrate that standard meshing strategies based on resolving the maximum wavenumber across the domain become computationally inefficient in multilayered configurations, where high wavenumbers are confined to localized subdomains. Through a systematic study of multilayer transmission problems, we show that no simple discretization rule based on the maximum wavenumber or material contrasts emerges. Instead, the wavenumber of the background (exterior) medium plays a dominant role in determining the optimal boundary resolution. Building on these insights, we propose an adaptive approach that achieves uniform accuracy and efficient computation across multiple layers. Numerical experiments for a range of multilayer configurations demonstrate the scalability and robustness of the proposed approach.

math.NA↗

arXiv2026

Imaging with super-resolution in changing random media

We develop an imaging algorithm that exploits strong scattering to achieve super-resolution in changing random media. The method processes large and diverse array datasets using sparse dictionary learning, clustering, and multidimensional scaling. Starting from random initializations, the algorithm reliably extracts the unknown medium properties necessary for accurate imaging using back-propagation, $\ell_2$ or $\ell_1$ methods. Remarkably, scattering enhances resolution beyond homogeneous medium limits. When abundant data are available, the algorithm allows the realization of super-resolution in imaging.

physics.optics↗

arXiv2025

Modeling measurements for quantitative imaging subsurface targets

We study ground-penetrating synthetic aperture radar measurements of scattering by targets located below a rough air-soil interface. By considering the inherent space/angle limitations of this imaging modality, we introduce a simplified model for measurements. This model assumes (i) first-order interactions between the target and the air-soil interface, (ii) scattering by the target below a flat air-soil interface, and (iii) a point target model. Using the method of fundamental solutions to simulate two-dimensional simulations of scalar waves for the direct scattering problem, we systematically study each of these data modeling assumptions. To test and validate these assumptions, we apply principal component analysis to approximately remove ground bounce signals from measurements and then apply Kirchhoff migration on that processed data to produce images. We show that images using this modeled data are nearly identical to those that use simulated measurements from the full direct scattering problem. In that way, we show that this model contains the essential information contained in measurements. Consequently, it provides a theoretical framework for understanding how inherent space/angle limitations affect subsurface imaging systems.

eess.SP↗

arXiv2024

Super-resolution in disordered media using neural networks

We propose a methodology that exploits large and diverse data sets to accurately estimate the ambient medium's Green's functions in strongly scattering media. Given these estimates, obtained with and without the use of neural networks, excellent imaging results are achieved, with a resolution that is better than that of a homogeneous medium. This phenomenon, also known as super-resolution, occurs because the ambient scattering medium effectively enhances the physical imaging aperture. This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible.

cs.LG↗

arXiv2023

Wave-informed dictionary learning for high-resolution imaging in complex media

We propose an approach for imaging in scattering media when large and diverse data sets are available. It has two steps. Using a dictionary learning algorithm the first step estimates the true Green's function vectors as columns in an unordered sensing matrix. The array data comes from many sparse sets of sources whose location and strength are not known to us. In the second step, the columns of the estimated sensing matrix are ordered for imaging using Multi-Dimensional Scaling with connectivity information derived from cross-correlations of its columns, as in time reversal. For these two steps to work together we need data from large arrays of receivers so the columns of the sensing matrix are incoherent for the first step, as well as from sub-arrays so that they are coherent enough to obtain the connectivity needed in the second step. Through simulation experiments, we show that the proposed approach is able to provide images in complex media whose resolution is that of a homogeneous medium.

cs.CV↗

arXiv2023

Synthetic aperture radar imaging below a random rough surface

Motivated by applications in unmanned aerial based ground penetrating radar for detecting buried landmines, we consider the problem of imaging small point like scatterers situated in a lossy medium below a random rough surface. Both the random rough surface and the absorption in the lossy medium significantly impede the target detection and imaging process. Using principal component analysis we effectively remove the reflection from the air-soil interface. We then use a modification of the classical synthetic aperture radar imaging functional to image the targets. This imaging method introduces a user-defined parameter, $δ$, which scales the resolution by $\sqrtδ$ allowing for target localization with sub wavelength accuracy. Numerical results in two dimensions illustrate the robustness of the approach for imaging multiple targets. However, the depth at which targets are detectable is limited due to the absorption in the lossy medium.

eess.SP↗

arXiv2023

Synthetic aperture imaging of dispersive targets

We introduce a dispersive point target model based on scattering by a particle in the far-field. The synthetic aperture imaging problem is then expanded to identify these targets and recover their locations and frequency dependent reflectivities. We show that Kirchhoff migration (KM) is able to identify dispersive point targets in an imaging region. However, KM predicts target locations that are shifted in range from their true locations. We derive an estimate for this range shift for a single target. We also show that because of this range shift we cannot recover the complex-valued frequency dependent reflectivity, but we can recover its absolute value and hence the radar cross-section (RCS) of the target. Simulation results show that we can detect, recover the approximate location, and recover the RCS for dispersive point targets thereby opening opportunities to classifying important differences between multiple targets such as their sizes or material compositions.

eess.SP↗

arXiv2022

Quantitative phase and absorption contrast imaging

We present an algorithm for coherent diffractive imaging with phaseless measurements. It treats the forward model as a combination of coherent and incoherent waves. The algorithm reconstructs absorption and phase contrast that quantifies the attenuation and the refraction of the waves propagating through an object. It requires coherent or partially coherent illuminations, and several detectors to record the intensity of the distorted wave that passes through the object under inspection. The diversity of illuminations, obtained by putting masks between the source and the object, provides enough information for imaging. The computational cost of our algorithm is linear in the number of pixels of the image. Therefore, it is efficient for high-resolution imaging. Our algorithm guarantees exact recovery if the image is sparse for a given basis. Numerical experiments in the setting of phaseless diffraction imaging of sparse objects validate the efficiency and the precision of the suggested algorithm.

physics.comp-ph↗

arXiv2022

Tunable high-resolution synthetic aperture radar imaging

We have recently introduced a modification of the multiple signal classification (MUSIC) method for synthetic aperture radar. This method depends on a tunable, user-defined parameter, $ε$, that allows for quantitative high-resolution imaging. It requires however, relative large single-to-noise ratios (SNR) to work effectively. Here, we first identify the fundamental mechanism in that method that produces high-resolution images. Then we introduce a modification to Kirchhoff Migration (KM) that uses the same mechanism to produces tunable, high-resolution images. This modified KM method can be applied to low SNR measurements. We show simulation results that demonstrate the features of this method.

eess.SP↗

arXiv2021

High-resolution, quantitative signal subspace imaging for synthetic aperture radar

We consider synthetic aperture radar imaging of a region containing point-like targets. Measurements are the set of frequency responses to scattering by the targets taken over a collection of individual spatial locations along the flight path making up the synthetic aperture. Because signal subspace imaging methods do not work on these measurements directly, we rearrange the frequency response at each spatial location using the Prony method and obtain a matrix that is suitable for these methods. We arrange the set of these Prony matrices as one block-diagonal matrix and introduce a signal subspace imaging method for it. We show that this signal subspace method yields high-resolution and quantitative images provided that the signal-to-noise ratio is sufficiently high. We give a resolution analysis for this imaging method and validate this theory using numerical simulations. Additionally, we show that this imaging method is stable to random perturbations to the travel times and validate this theory with numerical simulations using the random travel time model for random media.

math.AP↗

arXiv2021

Correlation based Imaging for rotating satellites

We consider imaging of fast moving small objects in space, such as low earth orbit satellites, which are also rotating around a fixed axis. The imaging system consists of ground based, asynchronous sources of radiation and several passive receivers above the dense atmosphere. We use the cross-correlation of the received signals to reduce distortions from ambient medium fluctuations. Imaging with correlations also has the advantage of not requiring any knowledge about the probing pulse and depends weakly on the emitter positions. We account for the target's orbital velocity by introducing the necessary Doppler compensation. To image a fast rotating object we also need to compensate for the rotation. We show that the rotation parameters can be extracted directly from the auto-correlation of the data before the formation of the image. We then investigate and analyze an imaging method that relies on backpropagating the cross-correlation data structure to two points rather than one, thus forming an interference matrix. The proposed imaging method consists of estimating the reflectivity as the top eigenvector of the migrated cross-correlation data interference matrix. We call this the rank-1 image and show that it provides superior image resolution compared to the usual single-point migration scheme for fast moving and rotating objects. Moreover, we observe a significant improvement in resolution due to the rotation leading to a diffraction limited resolution. We carry out a theoretical analysis that illustrates the role of the two point migration method as well as that of the inverse aperture and rotation in improving resolution. Extensive numerical simulations support the theoretical results.

eess.SP↗

arXiv2020

Fast signal recovery from quadratic measurements

We present a novel approach for recovering a sparse signal from cross-correlated data. Cross-correlations naturally arise in many fields of imaging, such as optics, holography and seismic interferometry. Compared to the sparse signal recovery problem that uses linear measurements, the unknown is now a matrix formed by the cross correlation of the unknown signal. Hence, the bottleneck for inversion is the number of unknowns that grows quadratically. The main idea of our proposed approach is to reduce the dimensionality of the problem by recovering only the diagonal of the unknown matrix, whose dimension grows linearly with the size of the problem. The keystone of the methodology is the use of an efficient {\em Noise Collector} that absorbs the data that come from the off-diagonal elements of the unknown matrix and that do not carry extra information about the support of the signal. This results in a linear problem whose cost is similar to the one that uses linear measurements. Our theory shows that the proposed approach provides exact support recovery when the data is not too noisy, and that there are no false positives for any level of noise. Moreover, our theory also demonstrates that when using cross-correlated data, the level of sparsity that can be recovered increases, scaling almost linearly with the number of data. The numerical experiments presented in the paper corroborate these findings.

eess.SP↗

arXiv2020

Staggered explicit-implicit time-discretization for elastodynamics with dissipative internal variables

An extension of the two-step staggered time discretization of linear elastodynamics in stress-velocity form to systems involving internal variables subjected to a possibly non-linear dissipative evolution is proposed. The original scheme is thus enhanced by another step for the internal variables which, in general, is implicit, although even this step might be explicit if no spatial gradients of the internal variables are involved. Using an abstract Banach-space formulation, a-priori estimates and convergence are proved under a CFL condition. The developed three-step scheme finds applications in various problems of continuum mechanics at small strain. Here, we consider in particular plasticity, viscoelasticity (creep), diffusion in poroelastic media, and damage.

math.NA↗

arXiv2020

Generalized correlation based Imaging for satellites

We consider imaging of fast moving small objects in space, such as low earth orbit satellites. The imaging system consists of ground based, asynchronous sources of radiation and several passive receivers above the dense atmosphere. We use the cross correlation of the received signals to reduce distortions from ambient medium fluctuations. Imaging with correlations also has the advantage of not requiring any knowledge about the probing pulse and depends weakly on the emitter positions. We account for the target's orbital velocity by introducing the necessary Doppler compensation. We show that over limited imaging regions, a constant Doppler factor can be used, resulting in an efficient data structure for the correlations of the recorded signals. We then investigate and analyze different imaging methods using the cross-correlation data structure. Specifically, we show that using a generalized two point migration of the cross correlation data, the top eigenvector of the migrated data matrix provides superior image resolution compared to the usual single-point migration scheme. We carry out a theoretical analysis that illustrates the role of the two point migration methods as well as that of the inverse aperture in improving resolution. Extensive numerical simulations support the theoretical results and assess the scope of the imaging methodology.

eess.SP↗

arXiv2020

Synthetic aperture imaging and motion estimation using tensor methods

We consider a synthetic aperture imaging configuration, such as synthetic aperture radar (SAR), where we want to first separate reflections from moving targets from those coming from a stationary background, and then to image separately the moving and the stationary reflectors. For this purpose, we introduce a representation of the data as a third order tensor formed from data coming from partially overlapping sub-apertures. We then apply a tensor robust principal component analysis (TRPCA) to the tensor data which separates them into the parts coming from the stationary and moving reflectors. Images are formed with the separated data sets. Our analysis shows a distinctly improved performance of TRPCA, compared to the usual matrix case. In particular, the tensor decomposition can identify motion features that are undetectable when using the conventional motion estimation methods, including matrix RPCA. We illustrate the performance of the method with numerical simulations in the X-band radar regime.

eess.SP↗