Related papers: Statistical Mechanics Approach to Sparse Noise Den…
We consider signal reconstruction from the norms of subspace components generalizing standard phase retrieval problems. In the deterministic setting, a closed reconstruction formula is derived when the subspaces satisfy certain cubature…
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…
The signal demixing problem seeks to separate a superposition of multiple signals into its constituent components. This paper studies a two-stage approach that first decompresses and subsequently deconvolves the noisy and undersampled…
Line spectral estimation theory aims to estimate the off-the-grid spectral components of a time signal with optimal precision. Recent results have shown that it is possible to recover signals having sparse line spectra from few temporal…
An analysis of the influence of missing samples in signals exhibiting sparsity in the Hermite transform domain is provided. Based on the statistical properties derived for the Hermite coefficients of randomly undersampled signal, the…
We derive fundamental sample complexity bounds for recovering sparse and structured signals for linear and nonlinear observation models including sparse regression, group testing, multivariate regression and problems with missing features.…
Supervised learning methods with missing data have been extensively studied not just due to the techniques related to low-rank matrix completion. Also in unsupervised learning one often relies on imputation methods. As a matter of fact,…
Broadband wireless channels usually have the sparse nature. Based on the assumption of Gaussian noise model, adaptive filtering algorithms for reconstruction sparse channels were proposed to take advantage of channel sparsity. However,…
Signal models formed as linear combinations of few atoms from an over-complete dictionary or few frame vectors from a redundant frame have become central to many applications in high dimensional signal processing and data analysis. A core…
Denoising Score Matching estimates the score of a noised version of a target distribution by minimizing a regression loss and is widely used to train the popular class of Denoising Diffusion Models. A well known limitation of Denoising…
Focusing on identification, this paper develops techniques to reconstruct zero and nonzero elements of a sparse parameter vector of a stochastic dynamic system under feedback control, for which the current input may depend on the past…
In this paper we suggest a new algorithm for determination of signal-to-noise ratio (SNR). SNR is a quantitative measure widely used in science and engineering. Generally, methods for determination of SNR are based on using of…
This paper introduces a novel approach for recovering sparse signals using sorted L1/L2 minimization. The proposed method assigns higher weights to indices with smaller absolute values and lower weights to larger values, effectively…
Learning unnormalized statistical models (e.g., energy-based models) is computationally challenging due to the complexity of handling the partition function. To eschew this complexity, noise-contrastive estimation~(NCE) has been proposed by…
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…
This paper concerns the problem of recovering an unknown but structured signal $x \in R^n$ from $m$ quadratic measurements of the form $y_r=|<a_r,x>|^2$ for $r=1,2,...,m$. We focus on the under-determined setting where the number of…
This paper discusses the problem of estimating a stochastic signal from nonlinear uncertain observations with time-correlated additive noise described by a first-order Markov process. Random deception attacks are assumed to be launched by…
Most physical data sets contain a stochastic contribution produced by measurement noise or other random sources along with the signal. Usually, neither the signal nor the noise are accurately known prior to the measurement so that both have…
Networked systems usually face different random uncertainties that make the performance of the least-squares (LS) linear filter decline significantly. For this reason, great attention has been paid to the search for other kinds of…
An l0-regularized linear regression for a sparse signal reconstruction is implemented based on the quadratic unconstrained binary optimization (QUBO) formulation. In this method, the signal values are quantized and expressed as bit…