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Recovery of an unknown sparse signal from a few of its projections is the key objective of compressed sensing. Often one comes across signals that are not ordinarily sparse but are sparse blockwise. Existing block sparse recovery algorithms…
Partial Least Squares (PLS) regression emerged as an alternative to ordinary least squares for addressing multicollinearity in a wide range of scientific applications. As multidimensional tensor data is becoming more widespread, tensor…
We propose a new algorithm for recovery of sparse signals from their compressively sensed samples. The proposed algorithm benefits from the strategy of gradual movement to estimate the positions of non-zero samples of sparse signal. We…
Support recovery of sparse signals from noisy measurements with orthogonal matching pursuit (OMP) has been extensively studied in the literature. In this paper, we show that for any $K$-sparse signal $\x$, if the sensing matrix $\A$…
Sampling rate is the bottleneck for spectrum sensing over multi-GHz bandwidth. Recent progress in compressed sensing (CS) initialized several sub-Nyquist rate approaches to overcome the problem. However, efforts to design CS reconstruction…
A well-known analysis of Tropp and Gilbert shows that orthogonal matching pursuit (OMP) can recover a k-sparse n-dimensional real vector from 4 k log(n) noise-free linear measurements obtained through a random Gaussian measurement matrix…
We propose a new method for reconstruction of sparse signals with and without noisy perturbations, termed the subspace pursuit algorithm. The algorithm has two important characteristics: low computational complexity, comparable to that of…
In this paper we discuss the variable selection method from \ell0-norm constrained regression, which is equivalent to the problem of finding the best subset of a fixed size. Our study focuses on two aspects, consistency and computation. We…
Partial least squares (PLS) regression combines dimensionality reduction and prediction using a latent variable model. Since partial least squares regression (PLS-R) does not require matrix inversion or diagonalization, it can be applied to…
The problem of 1-bit compressive sampling is addressed in this paper. We introduce an optimization model for reconstruction of sparse signals from 1-bit measurements. The model targets a solution that has the least l0-norm among all signals…
We address the recovery of sparse vectors in an overcomplete, linear and noisy multiple measurement framework, where the measurement matrix is known upto a permutation of its rows. We derive sparse Bayesian learning (SBL) based updates for…
Current orthogonal matching pursuit (OMP) algorithms calculate the correlation between two vectors using the inner product operation and minimize the mean square error, which are both suboptimal when there are non-Gaussian noises or…
A data analyst might worry about generalization if dropping a very small fraction of data points from a study could change its substantive conclusions. Checking this non-robustness directly poses a combinatorial optimization problem and is…
RIS-aided millimeter wave wireless systems benefit from robustness to blockage and enhanced coverage. In this paper, we study the ability of RIS to also provide enhanced localization capabilities as a by-product of communication. We…
We have developed an approximate signal recovery algorithm with low computational cost for compressed sensing on the basis of randomly constructed sparse measurement matrices. The law of large numbers and the central limit theorem suggest…
This paper introduces a simple efficient learning algorithms for general sequential decision making. The algorithm combines Optimism for exploration with Maximum Likelihood Estimation for model estimation, which is thus named OMLE. We prove…
We propose an algorithm to select parameter subset combinations that can be estimated using an ordinary least-squares (OLS) inverse problem formulation with a given data set. First, the algorithm selects the parameter combinations that…
We consider the problem of reconstructing rank-one matrices from random linear measurements, a task that appears in a variety of problems in signal processing, statistics, and machine learning. In this paper, we focus on the Alternating…
In the context of high-dimensional linear regression models, we propose an algorithm of exact support recovery in the setting of noisy compressed sensing where all entries of the design matrix are independent and identically distributed…
We consider the problem of reconstructing a sparse signal $x^0\in\R^n$ from a limited number of linear measurements. Given $m$ randomly selected samples of $U x^0$, where $U$ is an orthonormal matrix, we show that $\ell_1$ minimization…