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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.…
The recovery of sparsest overcomplete representation has recently attracted intensive research activities owe to its important potential in the many applied fields such as signal processing, medical imaging, communication, and so on. This…
We consider the problem of signal estimation (denoising) from a statistical mechanical perspective, using a relationship between the minimum mean square error (MMSE), of estimating a signal, and the mutual information between this signal…
Literatures in state space models focus on parametric inference and prediction, which fail if the state space model is not fully specified and the maximum likelihood estimation does not work. In this paper, we assume the state transition…
Compressed Sensing suggests that the required number of samples for reconstructing a signal can be greatly reduced if it is sparse in a known discrete basis, yet many real-world signals are sparse in a continuous dictionary. One example is…
The growing environmental footprint of artificial intelligence (AI), especially in terms of storage and computation, calls for more frugal and interpretable models. Sparse models (e.g., linear, neural networks) offer a promising solution by…
We consider the estimation of a signal from the knowledge of its noisy linear random Gaussian projections. A few examples where this problem is relevant are compressed sensing, sparse superposition codes, and code division multiple access.…
We consider the weak detection problem in a rank-one spiked Wigner data matrix where the signal-to-noise ratio is small so that reliable detection is impossible. We propose a hypothesis test on the presence of the signal by utilizing the…
We assume the direct sum <A> o <B> for the signal subspace. As a result of post- measurement, a number of operational contexts presuppose the a priori knowledge of the LB -dimensional "interfering" subspace <B> and the goal is to estimate…
We consider the sparse moment problem of learning a $k$-spike mixture in high-dimensional space from its noisy moment information in any dimension. We measure the accuracy of the learned mixtures using transportation distance. Previous…
In this paper we present a generic framework for the asymptotic performance analysis of subspace-based parameter estimation schemes. It is based on earlier results on an explicit first-order expansion of the estimation error in the signal…
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 consider a sparse high dimensional regression model where the goal is to recover a $k$-sparse unknown vector $\beta^*$ from $n$ noisy linear observations of the form $Y=X\beta^*+W \in \mathbb{R}^n$ where $X \in \mathbb{R}^{n \times p}$…
This paper is to study a signal-plus-noise model in high dimensional settings when the dimension and the sample size are comparable. Specifically, we assume that the noise has a general covariance matrix that allows for heteroskedasticity,…
In many real-world problems, recovering sparse signals from underdetermined linear systems remains a fundamental challenge. Although $\ell_1$ norm minimization is widely used, it suffers from estimation bias that prevents it from reaching…
This paper is concerned about sparse, continuous frequency estimation in line spectral estimation, and focused on developing gridless sparse methods which overcome grid mismatches and correspond to limiting scenarios of existing grid-based…
This paper considers sparse spiked covariance matrix models in the high-dimensional setting and studies the minimax estimation of the covariance matrix and the principal subspace as well as the minimax rank detection. The optimal rate of…
In this paper we consider the trace regression model where $n$ entries or linear combinations of entries of an unknown $m_1\times m_2$ matrix $A_0$ corrupted by noise are observed. We establish for the nuclear-norm penalized estimator of…
Accurate phase extraction from sinusoidal signals is a crucial task in various signal processing applications. While prior research predominantly addresses the case of asynchronous sampling with unknown signal frequency, this study focuses…
This paper develops theoretical results regarding noisy 1-bit compressed sensing and sparse binomial regression. We show that a single convex program gives an accurate estimate of the signal, or coefficient vector, for both of these models.…