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Classical results in sparse recovery guarantee the exact reconstruction of $s$-sparse signals under assumptions on the dictionary that are either too strong or NP-hard to check. Moreover, such results may be pessimistic in practice since…
In recent years, with the increase in renewable energy and storage penetration, power flow studies in low-voltage networks have become of interest in both industry and academia. Many studies use impedance represented by sequence components…
Graph Signal Processing (GSP) is an emerging research field that extends the concepts of digital signal processing to graphs. GSP has numerous applications in different areas such as sensor networks, machine learning, and image processing.…
Time domain simulation, i.e., modeling the system's evolution over time, is a crucial tool for studying and enhancing power system stability and dynamic performance. However, these simulations become computationally intractable for…
Compressed sensing is a central topic in signal processing with myriad applications, where the goal is to recover a signal from as few observations as possible. Iterative re-weighting is one of the fundamental tools to achieve this goal.…
This paper studies sparse covariance operator estimation for nonstationary processes with sharply varying marginal variance and small correlation lengthscale. We introduce a covariance operator estimator that adaptively thresholds the…
Spatial-temporal estimation of signals on graph edges is challenging because most conventional Graph Signal Processing techniques are defined on the graph nodes. Leveraging the Line Graph transform, the Line Graph Least Mean Square (LGLMS)…
The time periodic circuit theory is exploited to introduce an appropriate translation operator that is invariant under the change of the spatial unit cell. Useful properties of the operator are derived. By casting the problem in an…
We propose a novel numerical inversion algorithm for the coefficients of parabolic partial differential equations, based on model reduction. The study is motivated by the application of controlled source electromagnetic exploration, where…
We propose a decentralized online learning algorithm for distributed random inverse problems over network graphs with online measurements, and unifies the distributed parameter estimation in Hilbert spaces and the least mean square problem…
We consider and analyze applying a spectral inverse iteration algorithm and its subspace iteration variant for computing eigenpairs of an elliptic operator with random coefficients. With these iterative algorithms the solution is sought…
Identifying differential operators from data is essential for the mathematical modeling of complex physical and biological systems where massive datasets are available. These operators must be stable for accurate predictions for dynamics…
We address the inverse problem of identifying nonlocal interaction potentials in nonlinear aggregation-diffusion equations from noisy discrete trajectory data. Our approach involves formulating and solving a regularized variational problem,…
A new framework is proposed to study rank-structured matrices arising from discretizations of 2D and 3D elliptic operators. In particular, we introduce the notion of a graph-induced rank structure (GIRS) which aims to capture the fine low…
We consider the problem of learning a low-dimensional signal model from a collection of training samples. The mainstream approach would be to learn an overcomplete dictionary to provide good approximations of the training samples using…
In this paper, we consider the mixture of sparse linear regressions model. Let ${\beta}^{(1)},\ldots,{\beta}^{(L)}\in\mathbb{C}^n$ be $ L $ unknown sparse parameter vectors with a total of $ K $ non-zero coefficients. Noisy linear…
Time-varying graph signal recovery has been widely used in many applications, including climate change, environmental hazard monitoring, and epidemic studies. It is crucial to choose appropriate regularizations to describe the…
Sparse dictionary coding represents signals as linear combinations of a few dictionary atoms. It has been applied to images, time series, graph signals and multi-way spatio-temporal data by jointly employing temporal and spatial…
Many modern data analytics applications on graphs operate on domains where graph topology is not known a priori, and hence its determination becomes part of the problem definition, rather than serving as prior knowledge which aids the…
We establish the weak convergence of inertial Krasnoselskii-Mann iterations towards a common fixed point of a family of quasi-nonexpansive operators, along with estimates for the non-asymptotic rate at which the residuals vanish. Strong and…