Related papers: Multidimensional Gradient-MUSIC: A Global Nonconve…
This article deals with the problem of the statistical performance analysis of the MUSIC ( Multiple Signal Classification ) algorithm which is an eigen decomposition based method for the estimation of the angles of arrival of signals…
In this paper, we study the minimax optimization problem in the smooth and strongly convex-strongly concave setting when we have access to noisy estimates of gradients. In particular, we first analyze the stochastic Gradient Descent Ascent…
We study fundamental limits of first-order stochastic optimization in a range of nonconvex settings, including L-smooth functions satisfying Quasar-Convexity (QC), Quadratic Growth (QG), and Restricted Secant Inequalities (RSI). While the…
This paper determines to within a single measurement the minimum number of measurements required to successfully reconstruct a signal drawn from a Gaussian mixture model in the low-noise regime. The method is to develop upper and lower…
Random and structured noise both affect seismic data, hiding the reflections of interest (primaries) that carry meaningful geophysical interpretation. When the structured noise is composed of multiple reflections, its adaptive cancellation…
Recent advances in quantized compressed sensing and high-dimensional estimation have shown that signal recovery is even feasible under strong non-linear distortions in the observation process. An important characteristic of associated…
Traditional sampling theories consider the problem of reconstructing an unknown signal $x$ from a series of samples. A prevalent assumption which often guarantees recovery from the given measurements is that $x$ lies in a known subspace.…
Classical multidimensional scaling only works well when the noisy distances observed in a high dimensional space can be faithfully represented by Euclidean distances in a low dimensional space. Advanced models such as Maximum Variance…
For the problem of reconstructing a low-rank matrix from a few linear measurements, two classes of algorithms have been widely studied in the literature: convex approaches based on nuclear norm minimization, and non-convex approaches that…
This work analyzes the convergence of a class of smoothing-based gradient descent methods when applied to optimization problems. In particular, Gaussian smoothing is employed to define a nonlocal gradient that reduces high-frequency noise,…
An algorithm is proposed, analyzed, and tested for minimizing locally Lipschitz objective functions that may be nonconvex and/or nonsmooth. The algorithm, which is built upon the gradient-sampling methodology, is designed specifically for…
We propose Comprehensive Robust Dynamic Mode Decomposition (CR-DMD), a novel framework that robustifies the entire DMD process - from mode extraction to dimensional reduction - against mixed noise. Although standard DMD widely used for…
Super-resolution is a fundamental task in imaging, where the goal is to extract fine-grained structure from coarse-grained measurements. Here we are interested in a popular mathematical abstraction of this problem that has been widely…
Optimization problems occurring in a wide variety of physical design problems, including but not limited to optical engineering, quantum control, structural engineering, involve minimization of a simple cost function of the state of the…
This paper investigates total variation minimization in one spatial dimension for the recovery of gradient-sparse signals from undersampled Gaussian measurements. Recently established bounds for the required sampling rate state that uniform…
Large-scale nonsmooth optimization problems arise in many real-world applications, but obtaining exact function and subgradient values for these problems may be computationally expensive or even infeasible. In many practical settings, only…
This paper investigates the recovery of a spectrally sparse signal from its partially revealed noisy entries within the framework of spectral compressive sensing. Nonconvex optimization approaches have recently been proposed based on…
When recovering an unknown signal from noisy measurements, the computational difficulty of performing optimal Bayesian MMSE (minimum mean squared error) inference often necessitates the use of maximum a posteriori (MAP) inference, a special…
Optimization of sensor selection has been studied to monitor complex and large-scale systems with data-driven linear reduced-order modeling. An algorithm for greedy sensor selection is presented under the assumption of correlated noise in…
High-dimensional simulation optimization is notoriously challenging. We propose a new sampling algorithm that converges to a global optimal solution and suffers minimally from the curse of dimensionality. The algorithm consists of two…