Related papers: Recovering a Clipped Signal in Sparseland
Intensively growing approach in signal processing and acquisition, the Compressive Sensing approach, allows sparse signals to be recovered from small number of randomly acquired signal coefficients. This paper analyses some of the commonly…
Compressed sensing has a wide range of applications that include error correction, imaging, radar and many more. Given a sparse signal in a high dimensional space, one wishes to reconstruct that signal accurately and efficiently from a…
Sparse signals can be recovered from a reduced set of samples by using compressive sensing algorithms. In common methods the signal is recovered in the sparse domain. A method for the reconstruction of sparse signal which reconstructs the…
We address the problem of recovering a sparse signal from clipped or quantized measurements. We show how these two problems can be formulated as minimizing the distance to a convex feasibility set, which provides a convex and differentiable…
It is well known that $\ell_1$ minimization can be used to recover sufficiently sparse unknown signals from compressed linear measurements. In fact, exact thresholds on the sparsity, as a function of the ratio between the system dimensions,…
It is now well understood that (1) it is possible to reconstruct sparse signals exactly from what appear to be highly incomplete sets of linear measurements and (2) that this can be done by constrained L1 minimization. In this paper, we…
This work considers recovery of signals that are sparse over two bases. For instance, a signal might be sparse in both time and frequency, or a matrix can be low rank and sparse simultaneously. To facilitate recovery, we consider minimizing…
It is well known that $\ell_1$ minimization can be used to recover sufficiently sparse unknown signals from compressed linear measurements. In fact, exact thresholds on the sparsity, as a function of the ratio between the system dimensions,…
We propose and analyze an online algorithm for reconstructing a sequence of signals from a limited number of linear measurements. The signals are assumed sparse, with unknown support, and evolve over time according to a generic nonlinear…
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…
Compressed sensing is a technique for recovering an unknown sparse signal from a small number of linear measurements. When the measurement matrix is random, the number of measurements required for perfect recovery exhibits a phase…
Compressed sensing deals with the recovery of sparse signals from linear measurements. Without any additional information, it is possible to recover an $s$-sparse signal using $m \gtrsim s \log(d/s)$ measurements in a robust and stable way.…
Compressive Sensing, as an emerging technique in signal processing is reviewed in this paper together with its common applications. As an alternative to the traditional signal sampling, Compressive Sensing allows a new acquisition strategy…
The problem of the distributed recovery of jointly sparse signals has attracted much attention recently. Let us assume that the nodes of a network observe different sparse signals with common support; starting from linear, compressed…
In this article, we discuss a novel greedy algorithm for the recovery of compressive sampled signals under noisy conditions. Most of the greedy recovery algorithms proposed in the literature require sparsity of the signal to be known or…
This paper develops new theory and algorithms to recover signals that are approximately sparse in some general dictionary (i.e., a basis, frame, or over-/incomplete matrix) but corrupted by a combination of interference having a sparse…
The theory of Compressed Sensing, the emerging sampling paradigm 'that goes against the common wisdom', asserts that 'one can recover signals in Rn from far fewer samples or measurements, if the signal has a sparse representation in some…
The recovery of signals with finite-valued components from few linear measurements is a problem with widespread applications and interesting mathematical characteristics. In the compressed sensing framework, tailored methods have been…
In this paper, we consider the sparse phase retrieval problem, recovering an $s$-sparse signal $\bm{x}^{\natural}\in\mathbb{R}^n$ from $m$ phaseless samples $y_i=|\langle\bm{x}^{\natural},\bm{a}_i\rangle|$ for $i=1,\ldots,m$. Existing…
Compressive sensing is a methodology for the reconstruction of sparse or compressible signals using far fewer samples than required by the Nyquist criterion. However, many of the results in compressive sensing concern random sampling…