Related papers: Average performance of Orthogonal Matching Pursuit…
In this paper, we study the orthogonal least squares (OLS) algorithm for sparse recovery. On the one hand, we show that if the sampling matrix $\mathbf{A}$ satisfies the restricted isometry property (RIP) of order $K + 1$ with isometry…
Unions of subspaces provide a powerful generalization to linear subspace models for collections of high-dimensional data. To learn a union of subspaces from a collection of data, sets of signals in the collection that belong to the same…
Highly coherent sensing matrices arise in discretization of continuum problems such as radar and medical imaging when the grid spacing is below the Rayleigh threshold as well as in using highly coherent, redundant dictionaries as…
Sparse representation of astronomical images is discussed. It is shown that a significant gain in sparsity is achieved when particular mixed dictionaries are used for approximating these types of images with greedy selection strategies.…
Orthogonal time frequency space (OTFS) modulation outperforms orthogonal frequency division multiplexing (OFDM) in high-mobility scenarios. One challenge for OTFS massive MIMO is downlink channel estimation due to the large number of base…
A dedicated algorithm for sparse spectral representation of music sound is presented. The goal is to enable the representation of a piece of music signal, as a linear superposition of as few spectral components as possible. A representation…
To achieve high range resolution profile (HRRP), the geometric theory of diffraction (GTD) parametric model is widely used in stepped-frequency radar system. In the paper, a fast synthetic range profile algorithm, called orthogonal matching…
We consider the problem of recovering off-the-grid spikes from linear measurements. The state of the art Over-Parametrized Continuous Orthogonal Matching Pursuit (OP-COMP) with Projected Gradient Descent (PGD) successfully recovers those…
This paper addresses the sparse representation (SR) problem within a general Bayesian framework. We show that the Lagrangian formulation of the standard SR problem, i.e., $\mathbf{x}^\star=\arg\min_\mathbf{x} \lbrace \|…
Best-first search has been recently utilized for compressed sensing (CS) by the A* orthogonal matching pursuit (A*OMP) algorithm. In this work, we concentrate on theoretical and empirical analyses of A*OMP. We present a restricted isometry…
In this paper, we address the sparse multiple measurement vector (MMV) problem where the objective is to recover a set of sparse nonzero row vectors or indices of a signal matrix from incomplete measurements. Ideally, regardless of the…
We propose a class of greedy algorithms for weighted sparse recovery by considering new loss function-based generalizations of Orthogonal Matching Pursuit (OMP). Given a (regularized) loss function, the proposed algorithms alternate the…
We consider expected risk minimization problems when the range of the estimator is required to be nonnegative, motivated by the settings of maximum likelihood estimation (MLE) and trajectory optimization. To facilitate nonlinear…
In this paper, we consider the sparse phase retrieval problem, recovering an $s$-sparse signal $\bm{x}^{\natural}\in\mathbb{R}^n$ from $m$ phaseless samples $y_i=|\langle\bm{x}^{\natural},\bm{a}_i\rangle|$ for $i=1,\ldots,m$. Existing…
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…
Applying the theory of compressive sensing in practice always takes different kinds of perturbations into consideration. In this paper, the recovery performance of greedy pursuits with replacement for sparse recovery is analyzed when both…
The convergence and numerical analysis of a low memory implementation of the Orthogonal Matching Pursuit greedy strategy, which is termed Self Projected Matching Pursuit, is presented. This approach renders an iterative way of solving the…
Two popular examples of first-order optimization methods over linear spaces are coordinate descent and matching pursuit algorithms, with their randomized variants. While the former targets the optimization by moving along coordinates, the…
Compressed sensing has a wide range of applications that include error correction, imaging, radar and many more. Given a sparse signal in a high dimensional space, one wishes to reconstruct that signal accurately and efficiently from a…
Matching pursuit algorithms are an important class of algorithms in signal processing and machine learning. We present a blended matching pursuit algorithm, combining coordinate descent-like steps with stronger gradient descent steps, for…