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Line spectral estimation is the problem of recovering the frequencies and amplitudes of a mixture of a few sinusoids from equispaced samples. However, in a variety of signal processing problems arising in imaging, radar, and localization we…
We establish a sparsity in terms of $\ell_p$-summability and weighted $\ell_2$-summability for the coefficients of the Laguerre generalized piecewise-polynomial chaos expansion of solutions to parametric elliptic PDEs with log-Laplace…
Ultrasound imaging faces a trade-off between image quality and hardware complexity caused by dense transducers. Sparse arrays are one popular solution to mitigate this challenge. This work proposes an end-to-end optimization framework that…
A communication network can be modeled as a directed connected graph with edge weights that characterize performance metrics such as loss and delay. Network tomography aims to infer these edge weights from their pathwise versions measured…
Spike and slab priors play a key role in inducing sparsity for sparse signal recovery. The use of such priors results in hard non-convex and mixed integer programming problems. Most of the existing algorithms to solve the optimization…
Super-resolution theory aims to estimate the discrete components lying in a continuous space that constitute a sparse signal with optimal precision. This work investigates the potential of recent super-resolution techniques for spectral…
Tracer diffusion and hydrodynamic dispersion in two-dimensional fractures with self-affine roughness is studied by analytic and numerical methods. Numerical simulations were performed via the lattice-Boltzmann approach, using a new boundary…
How does one generalize differential geometric constructs such as curvature of a manifold to the discrete world of graphs and other combinatorial structures? This problem carries significant importance for analyzing models of discrete…
Pillar-based 3D object detection has gained traction in self-driving technology due to its speed and accuracy facilitated by the artificial densification of pillars for GPU-friendly processing. However, dense pillar processing fundamentally…
Regularization of ill-posed linear inverse problems via $\ell_1$ penalization has been proposed for cases where the solution is known to be (almost) sparse. One way to obtain the minimizer of such an $\ell_1$ penalized functional is via an…
The goal of compressed sensing is to reconstruct a sparse signal under a few linear measurements far less than the dimension of the ambient space of the signal. However, many real-life applications in physics and biomedical sciences carry…
When solving partial differential equations (PDEs) using finite difference or finite element methods, efficient solvers are required for handling large sparse linear systems. In this paper, a recursive sparse LU decomposition for matrices…
We develop a Bregman proximal gradient method for structure learning on linear structural causal models. While the problem is non-convex, has high curvature and is in fact NP-hard, Bregman gradient methods allow us to neutralize at least…
In this work, we introduce a new perspective on comparative image assessment by representing an image pair as a structured composition of its regions. In contrast, existing methods focus on whole image analysis, while implicitly relying on…
Relying on the classical connection between Backward Stochastic Differential Equations (BSDEs) and non-linear parabolic partial differential equations (PDEs), we propose a new probabilistic learning scheme for solving high-dimensional…
We address the problem of recovering a sparse signal from clipped or quantized measurements. We show how these two problems can be formulated as minimizing the distance to a convex feasibility set, which provides a convex and differentiable…
Indoor 3D object detection is an essential task in single image scene understanding, impacting spatial cognition fundamentally in visual reasoning. Existing works on 3D object detection from a single image either pursue this goal through…
Computed tomography is widely used to examine internal structures in a non-destructive manner. To obtain high-quality reconstructions, one typically has to acquire a densely sampled trajectory to avoid angular undersampling. However, many…
This paper presents a learnable solver tailored to iteratively solve sparse linear systems from discretized partial differential equations (PDEs). Unlike traditional approaches relying on specialized expertise, our solver streamlines the…
Graphs are naturally sparse objects that are used to study many problems involving networks, for example, distributed learning and graph signal processing. In some cases, the graph is not given, but must be learned from the problem and…