Related papers: The Sampling Rate-Distortion Tradeoff for Sparsity…

In signal processing and data recovery, reconstructing a signal from quadratic measurements poses a significant challenge, particularly in high-dimensional settings where measurements $m$ is far less than the signal dimension $n$ (i.e., $m…

The joint-sparse recovery problem aims to recover, from sets of compressed measurements, unknown sparse matrices with nonzero entries restricted to a subset of rows. This is an extension of the single-measurement-vector (SMV) problem widely…

Compressed Sensing suggests that the required number of samples for reconstructing a signal can be greatly reduced if it is sparse in a known discrete basis, yet many real-world signals are sparse in a continuous dictionary. One example is…

Many applications concern sparse signals, for example, detecting anomalies from the differences between consecutive images taken by surveillance cameras. This paper focuses on the problem of recovering a K-sparse signal x in N dimensions.…

In this paper we present a new algorithm for compressive sensing that makes use of binary measurement matrices and achieves exact recovery of ultra sparse vectors, in a single pass and without any iterations. Due to its noniterative nature,…

We consider the problem of robustly recovering a $k$-sparse coefficient vector from the Fourier series that it generates, restricted to the interval $[- \Omega, \Omega]$. The difficulty of this problem is linked to the superresolution…

In this paper we study the compressed sensing problem of recovering a sparse signal from a system of underdetermined linear equations when we have prior information about the probability of each entry of the unknown signal being nonzero. In…

Phase retrieval (PR) is a popular research topic in signal processing and machine learning. However, its performance degrades significantly when the measurements are corrupted by noise or outliers. To address this limitation, we propose a…

We know that compressive sensing can establish stable sparse recovery results from highly undersampled data under a restricted isometry property condition. In reality, however, numerous problems are coherent, and vast majority conventional…

We present improved sampling complexity bounds for stable and robust sparse recovery in compressed sensing. Our unified analysis based on l1 minimization encompasses the case where (i) the measurements are block-structured samples in order…

This paper describes performance bounds for compressed sensing (CS) where the underlying sparse or compressible (sparsely approximable) signal is a vector of nonnegative intensities whose measurements are corrupted by Poisson noise. In this…

Sparse recovery from linear Gaussian measurements has been the subject of much investigation since the breaktrough papers \cite{CRT:IEEEIT06} and \cite{donoho2006compressed} on Compressed Sensing. Application to sparse vectors and sparse…

We consider the problem of recovering fusion frame sparse signals from incomplete measurements. These signals are composed of a small number of nonzero blocks taken from a family of subspaces. First, we show that, by using a-priori…

We propose a new method for reconstruction of sparse signals with and without noisy perturbations, termed the subspace pursuit algorithm. The algorithm has two important characteristics: low computational complexity, comparable to that of…

Compressed sensing (CS) shows that a signal having a sparse or compressible representation can be recovered from a small set of linear measurements. In classical CS theory, the sampling matrix and representation matrix are assumed to be…

The goal of phaseless compressed sensing is to recover an unknown sparse or approximately sparse signal from the magnitude of its measurements. However, it does not take advantage of any support information of the original signal.…

The problem of estimating a sparse signal from low dimensional noisy observations arises in many applications, including super resolution, signal deconvolution, and radar imaging. In this paper, we consider a sparse signal model with…

In many applications we seek to recover signals from linear measurements far fewer than the ambient dimension, given the signals have exploitable structures such as sparse vectors or low rank matrices. In this paper we work in a general…

It is known that sparse recovery is possible if the number of measurements is in the order of the sparsity, but the corresponding decoders either lack polynomial decoding time or robustness to noise. Commonly, decoders that rely on a null…

The recently proposed modified-compressive sensing (modified-CS), which utilizes the partially known support as prior knowledge, significantly improves the performance of recovering sparse signals. However, modified-CS depends heavily on…