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Phase retrieval refers to a classical nonconvex problem of recovering a signal from its Fourier magnitude measurements. Inspired by the compressed sensing technique, signal sparsity is exploited in recent studies of phase retrieval to…
We propose and analyze an online algorithm for reconstructing a sequence of signals from a limited number of linear measurements. The signals are assumed sparse, with unknown support, and evolve over time according to a generic nonlinear…
This paper deals with sparse phase retrieval, i.e., the problem of estimating a vector from quadratic measurements under the assumption that few components are nonzero. In particular, we consider the problem of finding the sparsest vector…
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…
Separable multi-block convex optimization problem appears in many mathematical and engineering fields. In the first part of this paper, we propose an inertial proximal ADMM to solve a linearly constrained separable multi-block convex…
Recovery of arbitrarily positioned samples that are missing in sparse signals recently attracted significant research interest. Sparse signals with heavily corrupted arbitrary positioned samples could be analyzed in the same way as…
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 new algorithm to learn a dictionary for reconstructing and sparsely encoding signals from measurements without phase. Specifically, we consider the task of estimating a two-dimensional image from squared-magnitude measurements…
Given a linear system in a real or complex domain, linear regression aims to recover the model parameters from a set of observations. Recent studies in compressive sensing have successfully shown that under certain conditions, a linear…
This paper studies sequential methods for recovery of sparse signals in high dimensions. When compared to fixed sample size procedures, in the sparse setting, sequential methods can result in a large reduction in the number of samples…
The goal of Sparse Convex Optimization is to optimize a convex function $f$ under a sparsity constraint $s\leq s^*\gamma$, where $s^*$ is the target number of non-zero entries in a feasible solution (sparsity) and $\gamma\geq 1$ is an…
We consider the problem of sparse coding, where each sample consists of a sparse linear combination of a set of dictionary atoms, and the task is to learn both the dictionary elements and the mixing coefficients. Alternating minimization is…
In the problem of compressive phase retrieval, one wants to recover an approximately $k$-sparse signal $x \in \mathbb{C}^n$, given the magnitudes of the entries of $\Phi x$, where $\Phi \in \mathbb{C}^{m \times n}$. This problem has…
Line spectral estimation theory aims to estimate the off-the-grid spectral components of a time signal with optimal precision. Recent results have shown that it is possible to recover signals having sparse line spectra from few temporal…
In this paper, we consider a recursive estimation problem for linear regression where the signal to be estimated admits a sparse representation and measurement samples are only sequentially available. We propose a convergent parallel…
A major enterprise in compressed sensing and sparse approximation is the design and analysis of computationally tractable algorithms for recovering sparse, exact or approximate, solutions of underdetermined linear systems of equations. Many…
This work considers recovery of signals that are sparse over two bases. For instance, a signal might be sparse in both time and frequency, or a matrix can be low rank and sparse simultaneously. To facilitate recovery, we consider minimizing…
In many compressive sensing problems today, the relationship between the measurements and the unknowns could be nonlinear. Traditional treatment of such nonlinear relationships have been to approximate the nonlinearity via a linear model…
We introduce a \emph{batch} version of sparse recovery, where the goal is to report a sequence of vectors $A_1',\ldots,A_m' \in \mathbb{R}^n$ that estimate unknown signals $A_1,\ldots,A_m \in \mathbb{R}^n$ using a few linear measurements,…
We study the problem of recovering sparse signals from compressed linear measurements. This problem, often referred to as sparse recovery or sparse reconstruction, has generated a great deal of interest in recent years. To recover the…