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Identifying damage of structural systems is typically characterized as an inverse problem which might be ill-conditioned due to aleatory and epistemic uncertainties induced by measurement noise and modeling error. Sparse representation can…
This paper addresses sparse signal reconstruction under various types of structural side constraints with applications in multi-antenna systems. Side constraints may result from prior information on the measurement system and the sparse…
In this paper, we study the problem of recovering a group sparse vector from a small number of linear measurements. In the past the common approach has been to use various "group sparsity-inducing" norms such as the Group LASSO norm for…
We describe a probabilistic, {\it sublinear} runtime, measurement-optimal system for model-based sparse recovery problems through dimensionality reducing, {\em dense} random matrices. Specifically, we obtain a linear sketch $u\in \R^M$ of a…
We consider the problem of imaging sparse scenes from a few noisy data using an $l_1$-minimization approach. This problem can be cast as a linear system of the form $A \, \rho =b$, where $A$ is an $N\times K$ measurement matrix. We assume…
We introduce a novel optimization algorithm for image recovery under learned sparse and low-rank constraints, which we parameterize as weighted extensions of the $\ell_p^p$-vector and $\mathcal S_p^p$ Schatten-matrix quasi-norms for…
Restricted Isometry Property (RIP) is of fundamental importance in the theory of compressed sensing and forms the base of many exact and robust recovery guarantees in this field. A quantitative description of RIP involves bounding the…
The most widely used form of convolutional sparse coding uses an $\ell_1$ regularization term. While this approach has been successful in a variety of applications, a limitation of the $\ell_1$ penalty is that it is homogeneous across the…
The problem of finding sparse solutions to underdetermined systems of linear equations arises in several applications (e.g. signal and image processing, compressive sensing, statistical inference). A standard tool for dealing with sparse…
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…
The theory of (tight) wavelet frames has been extensively studied in the past twenty years and they are currently widely used for image restoration and other image processing and analysis problems. The success of wavelet frame based models,…
Recovering sparse vectors and low-rank matrices from noisy linear measurements has been the focus of much recent research. Various reconstruction algorithms have been studied, including $\ell_1$ and nuclear norm minimization as well as…
The sparse linear reconstruction problem is a core problem in signal processing which aims to recover sparse solutions to linear systems. The original problem regularized by the total number of nonzero components (also known as $L_0$…
As a conclusion in classical linear algebra, an underdetermined linear equations usually have an infinite number of solutions. The sparest one among these solutions is significant in many applications. This problem can be modeled as the…
Recovering an unknown but structured signal from its measurements is a challenging problem with significant applications in fields such as imaging restoration, wireless communications, and signal processing. In this paper, we consider the…
Recent work in adversarial robustness suggests that natural data distributions are localized, i.e., they place high probability in small volume regions of the input space, and that this property can be utilized for designing classifiers…
In this work, we consider the problem of recovering analysis-sparse signals from under-sampled measurements when some prior information about the support is available. We incorporate such information in the recovery stage by suitably tuning…
This paper confirms a surprising phenomenon first observed by Wright \textit{et al.} \cite{WYGSM_Face_2009_J} \cite{WM_denseError_2010_J} under different setting: given $m$ highly corrupted measurements $y = A_{\Omega \bullet} x^{\star} +…
Recovery of the sparsity pattern (or support) of an unknown sparse vector from a small number of noisy linear measurements is an important problem in compressed sensing. In this paper, the high-dimensional setting is considered. It is shown…
Sparse recovery is one of the most fundamental and well-studied inverse problems. Standard statistical formulations of the problem are provably solved by general convex programming techniques and more practical, fast (nearly-linear time)…