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Coded compressed sensing is an algorithmic framework tailored to sparse recovery in very large dimensional spaces. This framework is originally envisioned for the unsourced multiple access channel, a wireless paradigm attuned to…
Three properties of matrices: the spark, the mutual incoherence and the restricted isometry property have recently been introduced in the context of compressed sensing. We study these properties for matrices that are Kronecker products and…
Motivated by applications in unsourced random access, this paper develops a novel scheme for the problem of compressed sensing of binary signals. In this problem, the goal is to design a sensing matrix $A$ and a recovery algorithm, such…
Subspace clustering is a useful technique for many computer vision applications in which the intrinsic dimension of high-dimensional data is often smaller than the ambient dimension. Spectral clustering, as one of the main approaches to…
This paper derives sufficient conditions for local recovery of coordinate dictionaries comprising a Kronecker-structured dictionary that is used for representing $K$th-order tensor data. Tensor observations are assumed to be generated from…
Compressed sensing is a signal processing technique whereby the limits imposed by the Shannon--Nyquist theorem can be exceeded provided certain conditions are imposed on the signal. Such conditions occur in many real-world scenarios, and…
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…
Compressed sensing (CS) exploits the sparsity of a signal in order to integrate acquisition and compression. CS theory enables exact reconstruction of a sparse signal from relatively few linear measurements via a suitable nonlinear…
Many real-world data are naturally represented as a sparse reorderable matrix, whose rows and columns can be arbitrarily ordered (e.g., the adjacency matrix of a bipartite graph). Storing a sparse matrix in conventional ways requires an…
The Kronecker product is an invaluable tool for data-sparse representations of large networks and matrices with countless applications in machine learning, graph theory and numerical linear algebra. In some instances, the sparsity pattern…
The goal of compressed sensing is to learn a structured signal $x$ from a limited number of noisy linear measurements $y \approx Ax$. In traditional compressed sensing, "structure" is represented by sparsity in some known basis. Inspired by…
We investigate a reconstruction limit of compressed sensing for a reconstruction scheme based on the L1-norm minimization utilizing a correlated compression matrix with a statistical mechanics method. We focus on the compression matrix…
Increasing the imaging speed is a central aim in photoacoustic tomography. This issue is especially important in the case of sequential scanning approaches as applied for most existing optical detection schemes. In this work we address this…
We consider the problem of detecting whether a tensor signal having many missing entities lies within a given low dimensional Kronecker-Structured (KS) subspace. This is a matched subspace detection problem. Tensor matched subspace…
The choice of the sensing matrix is crucial in compressed sensing. Random Gaussian sensing matrices satisfy the restricted isometry property, which is crucial for solving the sparse recovery problem using convex optimization techniques.…
In this paper, we consider the problem of recovering an unknown sparse matrix X from the matrix sketch Y = AX B^T. The dimension of Y is less than that of X, and A and B are known matrices. This problem can be solved using standard…
Recent breakthrough results in compressed sensing (CS) have established that many high dimensional objects can be accurately recovered from a relatively small number of non- adaptive linear projection observations, provided that the objects…
A compressed sensing method consists of a rectangular measurement matrix, $M \in \mathbbm{R}^{m \times N}$ with $m \ll N$, together with an associated recovery algorithm, $\mathcal{A}: \mathbbm{R}^m \rightarrow \mathbbm{R}^N$. Compressed…
In this paper we consider the problem of recovering a high dimensional data matrix from a set of incomplete and noisy linear measurements. We introduce a new model that can efficiently restrict the degrees of freedom of the problem and is…
Expressing a matrix as the sum of a low-rank matrix plus a sparse matrix is a flexible model capturing global and local features in data popularized as Robust PCA (Candes et al., 2011; Chandrasekaran et al., 2009). Compressed sensing,…