Related papers: On Compressive Sensing in Coding Problems: A Rigor…

We consider the estimation of a signal from the knowledge of its noisy linear random Gaussian projections, a problem relevant in compressed sensing, sparse superposition codes or code division multiple access just to cite few. There has…

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.…

Sparse coding refers to the pursuit of the sparsest representation of a signal in a typically overcomplete dictionary. From a Bayesian perspective, sparse coding provides a Maximum a Posteriori (MAP) estimate of the unknown vector under a…

Minimum mean square error (MMSE) estimation of block sparse signals from noisy linear measurements is considered. Unlike in the standard compressive sensing setup where the non-zero entries of the signal are independently and uniformly…

The success of the compressed sensing paradigm has shown that a substantial reduction in sampling and storage complexity can be achieved in certain linear and non-adaptive estimation problems. It is therefore an advisable strategy for…

We investigate a power-constrained sensing matrix design problem for a compressed sensing framework. We adopt a mean square error (MSE) performance criterion for sparse source reconstruction in a system where the source-to-sensor channel…

We establish exact asymptotic expressions for the normalized mutual information and minimum mean-square-error (MMSE) of sparse linear regression in the sub-linear sparsity regime. Our result is achieved by a generalization of the adaptive…

Compressed sensing is a signal processing technique in which data is acquired directly in a compressed form. There are two modeling approaches that can be considered: the worst-case (Hamming) approach and a statistical mechanism, in which…

Compressed sensing typically deals with the estimation of a system input from its noise-corrupted linear measurements, where the number of measurements is smaller than the number of input components. The performance of the estimation…

Federated learning is a privacy-preserving approach to train a global model at a central server by collaborating with wireless devices, each with its own local training data set. In this paper, we present a compressive sensing approach for…

We consider generalized linear models in regimes where the number of nonzero components of the signal and accessible data points are sublinear with respect to the size of the signal. We prove a variational formula for the asymptotic mutual…

Inspired by compressive sensing principles, we propose novel error control coding techniques for communication systems. The information bits are encoded in the support and the non-zero entries of a sparse signal. By selecting a dictionary…

In recent years, a large amount of multi-disciplinary research has been conducted on sparse models and their applications. In statistics and machine learning, the sparsity principle is used to perform model selection---that is,…

In the first part of the series papers, we set out to answer the following question: given specific restrictions on a set of samplers, what kind of signal can be uniquely represented by the corresponding samples attained, as the foundation…

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.…

In the problem of learning mixtures of linear regressions, the goal is to learn a collection of signal vectors from a sequence of (possibly noisy) linear measurements, where each measurement is evaluated on an unknown signal drawn uniformly…

This paper studies a high-dimensional inference problem involving the matrix tensor product of random matrices. This problem generalizes a number of contemporary data science problems including the spiked matrix models used in sparse…

In compressed sensing one measures sparse signals directly in a compressed form via a linear transform and then reconstructs the original signal. However, it is often the case that the linear transform itself is known only approximately, a…

Mutual information (MI) is one of the most general ways to measure relationships between random variables, but estimating this quantity for complex systems is challenging. Denoising diffusion models have recently set a new bar for density…

We consider continuous-time sparse stochastic processes from which we have only a finite number of noisy/noiseless samples. Our goal is to estimate the noiseless samples (denoising) and the signal in-between (interpolation problem). By…