Related papers: Computable performance guarantees for compressed s…
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…
Recently, \cite{CRT,DonohoPol} theoretically analyzed the success of a polynomial $\ell_1$-optimization algorithm in solving an under-determined system of linear equations. In a large dimensional and statistical context \cite{CRT,DonohoPol}…
Efficient algorithms for the sparse solution of under-determined linear systems $Ax = b$ are known for matrices $A$ satisfying suitable assumptions like the restricted isometry property (RIP). Without such assumptions little is known and…
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…
As shown in [Blumensath and Davies 2009, Baraniuk et al. 2010], signals whose wavelet coefficients exhibit a rooted tree structure can be recovered using specially-adapted compressed sensing algorithms from just n=O(k) measurements, where k…
We study a weaker formulation of the nullspace property which guarantees recovery of sparse signals from linear measurements by l_1 minimization. We require this condition to hold only with high probability, given a distribution on the…
Compressive sensing predicts that sufficiently sparse vectors can be recovered from highly incomplete information. Efficient recovery methods such as $\ell_1$-minimization find the sparsest solution to certain systems of equations. Random…
This paper considers compressed sensing and affine rank minimization in both noiseless and noisy cases and establishes sharp restricted isometry conditions for sparse signal and low-rank matrix recovery. The analysis relies on a key…
An interesting topic in compressive sensing concerns problems of sensing and recovering signals with sparse representations in a dictionary. In this note, we study conditions of sensing matrices A for the L1-synthesis method to accurately…
Compressed sensing is a novel technique where one can recover sparse signals from the undersampled measurements. In this correspondence, a $K \times N$ measurement matrix for compressed sensing is deterministically constructed via additive…
The $\ell^0$ minimization of compressed sensing is often relaxed to $\ell^1$, which yields easy computation using the shrinkage mapping known as soft thresholding, and can be shown to recover the original solution under certain hypotheses.…
Recovering sparse vectors and low-rank matrices from noisy linear measurements has been the focus of much recent research. Various reconstruction algorithms have been studied, including $\ell_1$ and nuclear norm minimization as well as…
Compressed sensing is a signal processing method that acquires data directly in a compressed form. This allows one to make less measurements than what was considered necessary to record a signal, enabling faster or more precise measurement…
The article concerns compressed sensing methods in the quaternion algebra. We prove that it is possible to uniquely reconstruct - by $\ell_1$ norm minimization - a sparse quaternion signal from a limited number of its real linear…
In compressed sensing one measures sparse signals directly in a compressed form via a linear transform and then reconstructs the original signal. However, it is often the case that the linear transform itself is known only approximately, a…
In this paper we address the recovery conditions of weighted $\ell_p$ minimization for signal reconstruction from compressed sensing measurements when partial support information is available. We show that weighted $\ell_p$ minimization…
Compressed sensing is a technique for finding sparse solutions to underdetermined linear systems. This technique relies on properties of the sensing matrix such as the restricted isometry property. Sensing matrices that satisfy the…
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.…
Compressed sensing is a technique to sample compressible signals below the Nyquist rate, whilst still allowing near optimal reconstruction of the signal. In this paper we present a theoretical analysis of the iterative hard thresholding…
This paper provides novel results for the recovery of signals from undersampled measurements based on analysis $\ell_1$-minimization, when the analysis operator is given by a frame. We both provide so-called uniform and nonuniform recovery…