Related papers: Minimax Optimal Sparse Signal Recovery with Poisso…
The Multi-Reference Alignment (MRA) problem aims at the recovery of an unknown signal from repeated observations under the latent action of a group of cyclic isometries, in the presence of additive noise of high intensity $\sigma$. It is a…
Sparse modeling has been widely and successfully used in many applications such as computer vision, machine learning, and pattern recognition. Accompanied with those applications, significant research has studied the theoretical limits and…
In this paper we present a linear programming solution for sign pattern recovery of a sparse signal from noisy random projections of the signal. We consider two types of noise models, input noise, where noise enters before the random…
Compressive sensing predicts that sufficiently sparse vectors can be recovered from highly incomplete information. Efficient recovery methods such as $\ell_1$-minimization find the sparsest solution to certain systems of equations. Random…
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…
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…
In this paper, we study a new notion of scaled minimaxity for sparse estimation in high-dimensional linear regression model. We present more optimistic lower bounds than the one given by the classical minimax theory and hence improve on…
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.…
We consider the Orthogonal Least-Squares (OLS) algorithm for the recovery of a $m$-dimensional $k$-sparse signal from a low number of noisy linear measurements. The Exact Recovery Condition (ERC) in bounded noisy scenario is established for…
The problem of recovering the sparsity pattern of a fixed but unknown vector $\beta^* \in \real^p based on a set of $n$ noisy observations arises in a variety of settings, including subset selection in regression, graphical model selection,…
Recent research has studied the role of sparsity in high dimensional regression and signal reconstruction, establishing theoretical limits for recovering sparse models from sparse data. This line of work shows that $\ell_1$-regularized…
Most existing bounds for signal reconstruction from compressive measurements make the assumption of additive signal-independent noise. However in many compressive imaging systems, the noise statistics are more accurately represented by…
This paper describes performance bounds for compressed sensing (CS) where the underlying sparse or compressible (sparsely approximable) signal is a vector of nonnegative intensities whose measurements are corrupted by Poisson noise. In this…
A popular approach within the signal processing and machine learning communities consists in modelling signals as sparse linear combinations of atoms selected from a learned dictionary. While this paradigm has led to numerous empirical…
We investigate conditions for the unique recoverability of sparse integer-valued signals from a small number of linear measurements. Both the objective of minimizing the number of nonzero components, the so-called $\ell_0$-norm, as well as…
We formulate sparse support recovery as a salient set identification problem and use information-theoretic analyses to characterize the recovery performance and sample complexity. We consider a very general model where we are not restricted…
We consider the problem of dictionary learning under the assumption that the observed signals can be represented as sparse linear combinations of the columns of a single large dictionary matrix. In particular, we analyze the minimax risk of…
We investigate the reconstruction of multivariate functions from samples using sparse recovery techniques. For Square Root Lasso, Orthogonal Matching Pursuit, and Compressive Sampling Matching Pursuit, we demonstrate both theoretically and…
In this paper we derive information theoretic performance bounds to sensing and reconstruction of sparse phenomena from noisy projections. We consider two settings: output noise models where the noise enters after the projection and input…
We take an information theoretic perspective on a classical sparse-sampling noisy linear model and present an analytical expression for the mutual information, which plays central role in a variety of communications/processing problems.…