Related papers: Gridless Chirp Parameter Retrieval via Constrained…
Compressed sensing deals with the recovery of sparse signals from linear measurements. Without any additional information, it is possible to recover an $s$-sparse signal using $m \gtrsim s \log(d/s)$ measurements in a robust and stable way.…
We consider the inverse problem of recovering a continuous-domain function from a finite number of noisy linear measurements. The unknown signal is modeled as the sum of a slowly varying trend and a periodic or quasi-periodic seasonal…
We propose an approach based on quadratic approximations for solving general Mixed-Integer Nonlinear Programming (MINLP) problems. Specifically, our approach entails the global approximation of the epigraphs of constraint functions by means…
We consider the problem of recovering a lowrank matrix M from a small number of random linear measurements. A popular and useful example of this problem is matrix completion, in which the measurements reveal the values of a subset of the…
In this paper, we provide a method to recover off-the-grid frequencies of a signal in two-dimensional (2-D) line spectral estimation. Most of the literature in this field focuses on the case in which the only information is spectral…
We analyze integer linear programs which we obtain after discretizing two-dimensional subproblems arising from a trust-region algorithm for mixed integer optimal control problems with total variation regularization. We discuss NP-hardness…
The electrical network reconfiguration problem aims to minimize losses in a distribution system by adjusting switches while ensuring radial topology. The growing use of renewable energy and the complexity of managing modern power grids make…
Parameter estimation of gravitational wave data is often computationally expensive, requiring simplifying assumptions such as circularisation of binary orbits. Although, if included, the sub-dominant effects like orbital eccentricity may…
The Euclidean distance geometry problem arises in a wide variety of applications, from determining molecular conformations in computational chemistry to localization in sensor networks. When the distance information is incomplete, the…
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…
This paper develops a method to obtain the optimal value for the regularization coefficient in a general mixed-integer problem (MIP). This approach eliminates the cross-validation performed in the existing penalty techniques to obtain a…
This paper proposes the capped least squares regression with an adaptive resistance parameter, hence the name, adaptive capped least squares regression. The key observation is, by taking the resistant parameter to be data dependent, the…
We consider the problem of signal reconstruction from quadratic measurements that are encoded as +1 or -1 depending on whether they exceed a predetermined positive threshold or not. Binary measurements are fast to acquire and inexpensive in…
This paper considers the problem of optimum reconstruction in generalized sampling-reconstruction processes (GSRPs). We propose constrained GSRP, a novel framework that minimizes the reconstruction error for inputs in a subspace, subject to…
This work investigates the parameter estimation performance of super-resolution line spectral estimation using atomic norm minimization. The focus is on analyzing the algorithm's accuracy of inferring the frequencies and complex magnitudes…
We consider the problem of finding a sparse solution for an underdetermined linear system of equations when the known parameters on both sides of the system are subject to perturbation. This problem is particularly relevant to…
We consider structured minimization problems subject to smooth inequality constraints and present a flexible algorithm that combines interior point (IP) and proximal gradient schemes. While traditional IP methods cannot cope with nonsmooth…
Estimating the values of unknown parameters from corrupted measured data faces a lot of challenges in ill-posed problems. In such problems, many fundamental estimation methods fail to provide a meaningful stabilized solution. In this work,…
We develop a linearized boundary control method for the inverse boundary value problem of determining the damping coefficient in the damped wave equation. The objective is to reconstruct an unknown perturbation in a known background damping…
Image deconvolution is still to be a challenging ill-posed problem for recovering a clear image from a given blurry image, when the point spread function is known. Although competitive deconvolution methods are numerically impressive and…