Related papers: Spike detection from inaccurate samplings
In high-dimensional statistical inference in which the number of parameters to be estimated is larger than that of the holding data, regularized linear estimation techniques are widely used. These techniques have, however, some drawbacks.…
In many practical situations, the useful signal is contained in a low-dimensional subspace, drown in noise and interference. Many questions related to the estimation and detection of the useful signal arise. Because of their particular…
In this paper, we investigate the theoretical guarantees of penalized $\lun$ minimization (also called Basis Pursuit Denoising or Lasso) in terms of sparsity pattern recovery (support and sign consistency) from noisy measurements with…
We model and study the problem of localizing a set of sparse forcing inputs for linear dynamical systems from noisy measurements when the initial state is unknown. This problem is of particular relevance to detecting forced oscillations in…
This paper addresses the problem of identifying sparse linear time-invariant (LTI) systems from a single sample trajectory generated by the system dynamics. We introduce a Lasso-like estimator for the parameters of the system, taking into…
In this paper, we recover sparse signals from their noisy linear measurements by solving nonlinear differential inclusions, which is based on the notion of inverse scale space (ISS) developed in applied mathematics. Our goal here is to…
The problem of estimating a sparse signal from low dimensional noisy observations arises in many applications, including super resolution, signal deconvolution, and radar imaging. In this paper, we consider a sparse signal model with…
We introduce a novel framework for change point detection in spherical functional autoregressive (SPHAR) processes, enabling the identification of structural breaks in spatio-temporal random fields on the sphere. Our LASSO-regularized…
This note considers the problem of approximating the locations of dominant spikes for a probability measure from noisy spectrum measurements under the condition of residue signal, significant noise level, and no minimum spectrum separation.…
In this paper, we consider the problem of sparse signal detection based on partial support set estimation with compressive measurements in a distributed network. Multiple nodes in the network are assumed to observe sparse signals which…
This article analyzes the recovery performance of two popular finite dimensional approximations of the sparse spikes deconvolution problem over Radon measures. We examine in a unified framework both the L1 regularization (often referred to…
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…
Sparse regularization is a central technique for both machine learning (to achieve supervised features selection or unsupervised mixture learning) and imaging sciences (to achieve super-resolution). Existing performance guaranties assume a…
This paper studies sparse spikes deconvolution over the space of measures. We focus our attention to the recovery properties of the support of the measure, i.e. the location of the Dirac masses. For non-degenerate sums of Diracs, we show…
This paper studies the problem of exact localization of sparse (point or extended) objects with noisy data. The crux of the proposed approach consists of random illumination. Several recovery methods are analyzed: the Lasso, BPDN and the…
Spike sorting is a class of algorithms used in neuroscience to attribute the time occurences of particular electric signals, called action potential or spike, to neurons. We rephrase this problem as a particular optimization problem : Lasso…
We consider the problem of sparse signal recovery from noisy measurements. Many of frequently used recovery methods rely on some sort of tuning depending on either noise or signal parameters. If no estimates for either of them are…
We develop a novel method for detection of signals and reconstruction of images in the presence of random noise. The method uses results from percolation theory. We specifically address the problem of detection of multiple objects of…
We formulate the sparse classification problem of $n$ samples with $p$ features as a binary convex optimization problem and propose a cutting-plane algorithm to solve it exactly. For sparse logistic regression and sparse SVM, our algorithm…
Adaptive sampling results in dramatic improvements in the recovery of sparse signals in white Gaussian noise. A sequential adaptive sampling-and-refinement procedure called Distilled Sensing (DS) is proposed and analyzed. DS is a form of…