Related papers: Structure-Blind Signal Recovery

The problem of signal recovery from the autocorrelation, or equivalently, the magnitudes of the Fourier transform, is of paramount importance in various fields of engineering. In this work, for one-dimensional signals, we give conditions,…

This paper considers the problem of recovering the permutation of an n-dimensional random vector X observed in Gaussian noise. First, a general expression for the probability of error is derived when a linear decoder (i.e., linear estimator…

We consider the problem of estimating an unknown signal $x_0$ from noisy linear observations $y = Ax_0 + z\in R^m$. In many practical instances, $x_0$ has a certain structure that can be captured by a structure inducing convex function…

We propose a nonconvexly regularized convex model for linear regression problems under non-Gaussian noise. The cost function of the proposed model is designed with a possibly non-quadratic data fidelity term and a nonconvex regularizer via…

We consider the problem of recovering an unknown vector from noisy data with the help of projection estimates. The goal is to find a convex combination of these estimates with the minimal risk. We study an aggregation method based on the…

This paper proposes a novel approach to robust radar detection of range-spread targets embedded in Gaussian noise with unknown covariance matrix. The idea is to model the useful target echo in each range cell as the sum of a coherent signal…

We consider the problem of estimating convex boundaries from blurred and noisy observations. In our model, the convolution of an intensity function $f$ is observed with additive Gaussian white noise. The function $f$ is assumed to have…

We address the problem of blind gain and phase calibration of a sensor array from ambient noise. The key motivation is to ease the calibration process by avoiding a complex procedure setup. We show that computing the sample covariance…

Many applications have benefited remarkably from low-dimensional models in the recent decade. The fact that many signals, though high dimensional, are intrinsically low dimensional has given the possibility to recover them stably from a…

We initiate the study of stochastic optimization with oblivious noise, broadly generalizing the standard heavy-tailed noise setup. In our setting, in addition to random observation noise, the stochastic gradient may be subject to…

We consider problem of signal detection in Gaussian white noise. Test statistics are linear combinations of squares of estimators of Fourier coefficients or $\mathbb{L}_2$-norms of kernel estimators. We point out necessary and sufficient…

Existing convex relaxation-based approaches to reconstruction in compressed sensing assume that noise in the measurements is independent of the signal of interest. We consider the case of noise being linearly correlated with the signal and…

We discuss two new methods of recovery of sparse signals from noisy observation based on $\ell_1$- minimization. They are closely related to the well-known techniques such as Lasso and Dantzig Selector. However, these estimators come with…

We consider the problem of exact support recovery of sparse signals via noisy measurements. The main focus is the sufficient and necessary conditions on the number of measurements for support recovery to be reliable. By drawing an analogy…

We derive a maximum a posteriori estimator for the linear observation model, where the signal and noise covariance matrices are both uncertain. The uncertainties are treated probabilistically by modeling the covariance matrices with prior…

We propose an estimation procedure for linear functionals based on Gaussian model selection techniques. We show that the procedure is adaptive, and we give a non asymptotic oracle inequality for the risk of the selected estimator with…

Uncovering causal relationships is a fundamental problem across science and engineering. However, most existing causal discovery methods assume acyclicity and direct access to the system variables -- assumptions that fail to hold in many…

This work deals with the problem of distributed data acquisition under non-linear communication constraints. More specifically, we consider a model setup where $M$ distributed nodes take individual measurements of an unknown structured…

We investigate minimax testing for detecting local signals or linear combinations of such signals when only indirect data is available. Naturally, in the presence of noise, signals that are too small cannot be reliably detected. In a…

Consider the Gaussian vector model with mean value {\theta}. We study the twin problems of estimating the number |{\theta}|_0 of non-zero components of {\theta} and testing whether |{\theta}|_0 is smaller than some value. For testing, we…