Related papers: Basis Pursuit Denoise with Nonsmooth Constraints
This paper develops a data-driven time-limited h2 model reduction method for discrete-time linear time-invariant systems. Specifically, we formulate and solve a regularized time-limited h2 model reduction problem using only noisy impulse…
We study the problem of sparse reconstruction from noisy undersampled measurements when the following two things are available. (1) We are given partial, and partly erroneous, knowledge of the signal's support, denoted by $T$. (2) We are…
Sparse system identification is the data-driven process of obtaining parsimonious differential equations that describe the evolution of a dynamical system, balancing model complexity and accuracy. There has been rapid innovation in system…
In recent years, decentralized sensor networks have garnered significant attention in the field of state estimation owing to enhanced robustness, scalability, and fault tolerance. Optimal fusion performance can be achieved under fully…
Motivated by $\ell_p$-optimization arising from sparse optimization, high dimensional data analytics and statistics, this paper studies sparse properties of a wide range of $p$-norm based optimization problems with $p > 1$, including…
Many dynamical systems are difficult or impossible to model using high fidelity physics based models. Consequently, researchers are relying more on data driven models to make predictions and forecasts. Based on limited training data,…
In this paper, we present a unified and general framework for analyzing the batch updating approach to nonlinear, high-dimensional optimization. The framework encompasses all the currently used batch updating approaches, and is applicable…
We study the problem of estimating low-rank matrices from linear measurements (a.k.a., matrix sensing) through nonconvex optimization. We propose an efficient stochastic variance reduced gradient descent algorithm to solve a nonconvex…
Natural signals and images are well-known to be approximately sparse in transform domains such as Wavelets and DCT. This property has been heavily exploited in various applications in image processing and medical imaging. Compressed sensing…
Translating machine learning algorithms into clinical applications requires addressing challenges related to interpretability, such as accounting for the effect of confounding variables (or metadata). Confounding variables affect the…
Building on recent advances in Bayesian statistics and image denoising, we propose Noise2Score3D, a fully unsupervised framework for point cloud denoising that addresses the critical challenge of limited availability of clean data.…
Diffusion models have found valuable applications in anomaly detection by capturing the nominal data distribution and identifying anomalies via reconstruction. Despite their merits, they struggle to localize anomalies of varying scales,…
We develop a general framework for state estimation in systems modeled with noise-polluted continuous time dynamics and discrete time noisy measurements. Our approach is based on maximum likelihood estimation and employs the calculus of…
We know that compressive sensing can establish stable sparse recovery results from highly undersampled data under a restricted isometry property condition. In reality, however, numerous problems are coherent, and vast majority conventional…
Building on recent advances in Bayesian statistics and image denoising, we propose Noise2Score3D, a fully unsupervised framework for point cloud denoising. Noise2Score3D learns the score function of the underlying point cloud distribution…
We analyze the training dynamics for deep linear networks using a new metric - layer imbalance - which defines the flatness of a solution. We demonstrate that different regularization methods, such as weight decay or noise data…
Performance of regularized least-squares estimation in noisy compressed sensing is analyzed in the limit when the dimensions of the measurement matrix grow large. The sensing matrix is considered to be from a class of random ensembles that…
To streamline fast-track processing of large data volumes, we have developed a deep learning approach to deblend seismic data in the shot domain based on a practical strategy for generating high-quality training data along with a list of…
This paper considers the minimization of a continuously differentiable function over a cardinality constraint. We focus on smooth and relatively smooth functions. These smoothness criteria result in new descent lemmas. Based on the new…
This work investigates the use of machine learning applied to the beam tracking problem in 5G networks and beyond. The goal is to decrease the overhead associated to MIMO millimeter wave beamforming. In comparison to beam selection (also…