Related papers: On the Doubly Sparse Compressed Sensing Problem
Compressive sensing is a novel approach that linearly samples sparse or compressible signals at a rate much below the Nyquist-Shannon sampling rate and outperforms traditional signal processing techniques in acquiring and reconstructing…
Compressed sensing is a theory which guarantees the exact recovery of sparse signals from a small number of linear projections. The sampling schemes suggested by current compressed sensing theories are often of little practical relevance…
This work proposes a research problem of finding sparse solution of undetermined Linear system with some applications. Two approaches how to solve the compressive sensing problem: using l_1 approach , the l_q approach with 0 < q < 1.…
The problem central to sparse recovery and compressive sensing is that of stable sparse recovery: we want a distribution of matrices A in R^{m\times n} such that, for any x \in R^n and with probability at least 2/3 over A, there is an…
The problem of recovering a structured signal from its linear measurements in the presence of speckle noise is studied. This problem appears in many imaging systems such as synthetic aperture radar and optical coherence tomography. The…
Blind Compressed Sensing (BCS) is an extension of Compressed Sensing (CS) where the optimal sparsifying dictionary is assumed to be unknown and subject to estimation (in addition to the CS sparse coefficients). Since the emergence of BCS,…
We proposed a weighted l1 minimization to recover a sparse signal vector and the corrupted noise vector from a linear measurement when the sensing matrix A is an m by n row i.i.d subgaussian matrix. We obtain both uniform and nonuniform…
In this paper, we study the problem of sparse vector recovery at the fusion center of a sensor network from linear sensor measurements when there is missing data. In the presence of missing data, the random sampling approach employed in…
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,…
We are motivated by problems that arise in a number of applications such as Online Marketing and explosives detection, where the observations are usually modeled using Poisson statistics. We model each observation as a Poisson random…
The goal of compressive sensing is efficient reconstruction of data from few measurements, sometimes leading to a categorical decision. If only classification is required, reconstruction can be circumvented and the measurements needed are…
Compressed sensing aims at reconstructing sparse signals from significantly reduced number of samples, and a popular reconstruction approach is $\ell_1$-norm minimization. In this correspondence, a method called orthonormal expansion is…
This chapter gives an overview over recovery guarantees for total variation minimization in compressed sensing for different measurement scenarios. In addition to summarizing the results in the area, we illustrate why an approach that is…
Compressed sensing aims to undersample certain high-dimensional signals, yet accurately reconstruct them by exploiting signal characteristics. Accurate reconstruction is possible when the object to be recovered is sufficiently sparse in a…
This short note proves the $\ell_2-\ell_1$ instance optimality of a $\ell_1/\ell_1$ solver, i.e a variant of \emph{basis pursuit denoising} with a $\ell_1$ fidelity constraint, when applied to the estimation of sparse (or compressible)…
The task of compressed sensing is to recover a sparse vector from a small number of linear and non-adaptive measurements, and the problem of finding a suitable measurement matrix is very important in this field. While most recent works…
Consider the problem of recovering an unknown signal from undersampled measurements, given the knowledge that the signal has a sparse representation in a specified dictionary $D$. This problem is now understood to be well-posed and…
Compressed sensing is a relatively new mathematical paradigm that shows a small number of linear measurements are enough to efficiently reconstruct a large dimensional signal under the assumption the signal is sparse. Applications for this…
Sparse support recovery (SSR) is an important part of the compressive sensing (CS). Most of the current SSR methods are with the full information measurements. But in practice the amplitude part of the measurements may be seriously…
In compressed sensing, in order to recover a sparse or nearly sparse vector from possibly noisy measurements, the most popular approach is $\ell_1$-norm minimization. Upper bounds for the $\ell_2$- norm of the error between the true and…