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This paper examines the ability of greedy algorithms to estimate a block sparse parameter vector from noisy measurements. In particular, block sparse versions of the orthogonal matching pursuit and thresholding algorithms are analyzed under…
Greedy first-order methods, such as coordinate descent with Gauss-Southwell rule or matching pursuit, have become popular in optimization due to their natural tendency to propose sparse solutions and their refined convergence guarantees. In…
We study sparse approximate solutions to convex optimization problems. It is known that in many engineering applications researchers are interested in an approximate solution of an optimization problem as a linear combination of elements…
In the context of Gaussian conditioning, greedy algorithms iteratively select the most informative measurements, given an observed Gaussian random variable. However, the convergence analysis for conditioning Gaussian random variables…
We propose a randomized greedy search algorithm to find a point estimate for a random partition based on a loss function and posterior Monte Carlo samples. Given the large size and awkward discrete nature of the search space, the…
Sign truncated matching pursuit (STrMP) algorithm is presented in this paper. STrMP is a new greedy algorithm for the recovery of sparse signals from the sign measurement, which combines the principle of consistent reconstruction with…
The orthogonal matching pursuit (OMP) is an algorithm to solve sparse approximation problems. Sufficient conditions for exact recovery are known with and without noise. In this paper we investigate the applicability of the OMP for the…
Several sparsity-constrained algorithms such as Orthogonal Matching Pursuit or the Frank-Wolfe algorithm with sparsity constraints work by iteratively selecting a novel atom to add to the current non-zero set of variables. This selection…
We consider a distributed compressed sensing scenario where many sensors measure correlated sparse signals and the sensors are connected through a network. Correlation between sparse signals is modeled by a partial common support-set. For…
It is now well understood that (1) it is possible to reconstruct sparse signals exactly from what appear to be highly incomplete sets of linear measurements and (2) that this can be done by constrained L1 minimization. In this paper, we…
It is well known that $\ell_1$ minimization can be used to recover sufficiently sparse unknown signals from compressed linear measurements. In fact, exact thresholds on the sparsity, as a function of the ratio between the system dimensions,…
This paper deals with the design of a sensing matrix along with a sparse recovery algorithm by utilizing the probability-based prior information for compressed sensing system. With the knowledge of the probability for each atom of the…
Greedy algorithms are widely used for problems in machine learning such as feature selection and set function optimization. Unfortunately, for large datasets, the running time of even greedy algorithms can be quite high. This is because for…
Compressive Sensing (CS) is a new paradigm for the efficient acquisition of signals that have sparse representation in a certain domain. Traditionally, CS has provided numerous methods for signal recovery over an orthonormal basis. However,…
In this paper we introduce a nonuniform sparsity model and analyze the performance of an optimized weighted $\ell_1$ minimization over that sparsity model. In particular, we focus on a model where the entries of the unknown vector fall into…
Recovery of sparse signals from compressed measurements constitutes an l0 norm minimization problem, which is unpractical to solve. A number of sparse recovery approaches have appeared in the literature, including l1 minimization…
Models based on recursive adaptive partitioning such as decision trees and their ensembles are popular for high-dimensional regression as they can potentially avoid the curse of dimensionality. Because empirical risk minimization (ERM) is…
Existing approaches to compressive sensing of frequency-sparse signals focuses on signal recovery rather than spectral estimation. Furthermore, the recovery performance is limited by the coherence of the required sparsity dictionaries and…
This paper presents an algorithm tailored for the efficient recovery of sparse probability measures incorporating $\ell_0$-sparse regularization within the probability simplex constraint. Employing the Bregman proximal gradient method, our…
Orthogonal Matching Pursuit (OMP) has been a powerful method in sparse signal recovery and approximation. However, OMP suffers computational issues when the signal has a large number of non-zeros. This paper advances OMP and its extension…