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Compressed Sensing aims to capture attributes of a sparse signal using very few measurements. Cand\`{e}s and Tao showed that sparse reconstruction is possible if the sensing matrix acts as a near isometry on all $\boldsymbol{k}$-sparse…

Orthogonal Matching Pursuit (OMP) is the canonical greedy algorithm for sparse approximation. In this paper we demonstrate that the restricted isometry property (RIP) can be used for a very straightforward analysis of OMP. Our main…

Some consequences of the Restricted Isometry Property (RIP) of matrices have been applied to develop a greedy algorithm called "ROMP" (Regularized Orthogonal Matching Pursuit) to recover sparse signals and to approximate non-sparse ones.…

We propose a novel method for compressed sensing recovery using untrained deep generative models. Our method is based on the recently proposed Deep Image Prior (DIP), wherein the convolutional weights of the network are optimized to match…

In recent studies on sparse modeling, $l_q$ ($0<q<1$) regularized least squares regression ($l_q$LS) has received considerable attention due to its superiorities on sparsity-inducing and bias-reduction over the convex counterparts. In this…

In recent years, unfolding iterative algorithms as neural networks has become an empirical success in solving sparse recovery problems. However, its theoretical understanding is still immature, which prevents us from fully utilizing the…

For compressive sensing of dynamic sparse signals, we develop an iterative pursuit algorithm. A dynamic sparse signal process is characterized by varying sparsity patterns over time/space. For such signals, the developed algorithm is able…

In this paper, we propose a general framework for the asymptotic analysis of node-based verification-based algorithms. In our analysis we tend the signal length $n$ to infinity. We also let the number of non-zero elements of the signal $k$…

The recovery of sparse data is at the core of many applications in machine learning and signal processing. While such problems can be tackled using $\ell_1$-regularization as in the LASSO estimator and in the Basis Pursuit approach,…

This paper gives a precise characterization of the fundamental limits of adaptive sensing for diverse estimation and testing problems concerning sparse signals. We consider in particular the setting introduced in (IEEE Trans. Inform. Theory…

This paper studies a sparse signal recovery task in time-varying (time-adaptive) environments. The contribution of the paper to sparsity-aware online learning is threefold; first, a Generalized Thresholding (GT) operator, which relates to…

Sign truncated matching pursuit (STrMP) algorithm is presented in this paper. STrMP is a new greedy algorithm for the recovery of sparse signals from the sign measurement, which combines the principle of consistent reconstruction with…

Compressed sensing (CS) theory considers the restricted isometry property (RIP) as a sufficient condition for measurement matrix which guarantees the recovery of any sparse signal from its compressed measurements. The RIP condition also…

In this paper, a new nonlinear filter based on sparse-grid quadrature method has been proposed. The proposed filter is named as adaptive sparse-grid Gauss-Hermite filter (ASGHF). Ordinary sparse-grid technique treats all the dimensions…

This paper concerns the problem of 1-bit compressed sensing, where the goal is to estimate a sparse signal from a few of its binary measurements. We study a non-convex sparsity-constrained program and present a novel and concise analysis…

In the theory of compressed sensing, restricted isometry analysis has become a standard tool for studying how efficiently a measurement matrix acquires information about sparse and compressible signals. Many recovery algorithms are known to…

Hardware trends have motivated the development of mixed precision algo-rithms in numerical linear algebra, which aim to decrease runtime while maintaining acceptable accuracy. One recent development is the development of an adaptive…

This paper proposes a simple adaptive sensing and group testing algorithm for sparse signal recovery. The algorithm, termed Compressive Adaptive Sense and Search (CASS), is shown to be near-optimal in that it succeeds at the lowest possible…

The problem of 1-bit compressive sampling is addressed in this paper. We introduce an optimization model for reconstruction of sparse signals from 1-bit measurements. The model targets a solution that has the least l0-norm among all signals…

We consider the problem of compressed sensing and of (real-valued) phase retrieval with random measurement matrix. We derive sharp asymptotics for the information-theoretically optimal performance and for the best known polynomial algorithm…