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The topic of recovery of a structured model given a small number of linear observations has been well-studied in recent years. Examples include recovering sparse or group-sparse vectors, low-rank matrices, and the sum of sparse and low-rank…
Sparse signal reconstruction algorithms have attracted research attention due to their wide applications in various fields. In this paper, we present a simple Bayesian approach that utilizes the sparsity constraint and a priori statistical…
This paper explores robust recovery of a superposition of $R$ distinct complex exponential functions from a few random Gaussian projections. We assume that the signal of interest is of $2N-1$ dimensional and $R<<2N-1$. This framework covers…
We study robust PCA for the fully observed setting, which is about separating a low rank matrix $\boldsymbol{L}$ and a sparse matrix $\boldsymbol{S}$ from their sum $\boldsymbol{D}=\boldsymbol{L}+\boldsymbol{S}$. In this paper, a new…
We investigate the sparse recovery problem of reconstructing a high-dimensional non-negative sparse vector from lower dimensional linear measurements. While much work has focused on dense measurement matrices, sparse measurement schemes are…
We consider the high-dimensional sparse linear regression problem of accurately estimating a sparse vector using a small number of linear measurements that are contaminated by noise. It is well known that the standard cadre of…
Common ISAR radar images and signals can be reconstructed from much fewer samples than the sampling theorem requires since they are usually sparse. Unavailable randomly positioned samples can result from heavily corrupted parts of the…
This paper considers the problem of recovery of a low-rank matrix in the situation when most of its entries are not observed and a fraction of observed entries are corrupted. The observations are noisy realizations of the sum of a low rank…
Asynchronous parallel computing and sparse recovery are two areas that have received recent interest. Asynchronous algorithms are often studied to solve optimization problems where the cost function takes the form $\sum_{i=1}^M f_i(x)$,…
Sparse signal recovery based on nonconvex and nonsmooth optimization problems has significant applications and demonstrates superior performance in signal processing and machine learning. This work deals with a scale-invariant…
This paper develops new theory and algorithms to recover signals that are approximately sparse in some general dictionary (i.e., a basis, frame, or over-/incomplete matrix) but corrupted by a combination of interference having a sparse…
Greedy algorithm are in widespread use for sparse recovery because of its efficiency. But some evident flaws exists in most popular greedy algorithms, such as CoSaMP, which includes unreasonable demands on prior knowledge of target signal…
We study the spectral recovery problem for dynamical sampling on a finite cyclic grid. Given time snapshots obtained from a fixed uniform spatial subsampling of the orbit $x_{\ell}=A^{\ell}f$, we aim to recover the spectrum of the unknown…
The sparsity in levels model recently inspired a new generation of effective acquisition and reconstruction modalities for compressive imaging. Moreover, it naturally arises in various areas of signal processing such as parallel…
This paper presents a new approach to the recovery of a spectrally sparse signal (SSS) from partially observed entries, focusing on challenges posed by large-scale data and heavy noise environments. The SSS reconstruction can be formulated…
In this paper, we consider the challenge of reconstructing jointly sparse vectors from linear measurements. Firstly, we show that by utilizing the rank of the output data matrix we can reduce the problem to a full column rank case. This…
This paper investigates the problem of recovering the support of structured signals via adaptive compressive sensing. We examine several classes of structured support sets, and characterize the fundamental limits of accurately recovering…
We study the robust matrix completion problem for the low-rank Hankel matrix, which detects the sparse corruptions caused by extreme outliers while we try to recover the original Hankel matrix from the partial observation. In this paper, we…
Analysis based reconstruction has recently been introduced as an alternative to the well-known synthesis sparsity model used in a variety of signal processing areas. In this paper we convert the analysis exact-sparse reconstruction problem…
We consider the problem of reconstructing an infinite set of sparse, finite-dimensional vectors, that share a common sparsity pattern, from incomplete measurements. This is in contrast to the work [17], where the single vector signal can be…