Related papers: Uniform Recovery Bounds for Structured Random Matr…
We propose novel necessary and sufficient conditions for a sensing matrix to be "$s$-good" - to allow for exact $\ell_1$-recovery of sparse signals with $s$ nonzero entries when no measurement noise is present. Then we express the error…
Compressed sensing (sparse signal recovery) often encounters nonnegative data (e.g., images). Recently we developed the methodology of using (dense) Compressed Counting for recovering nonnegative K-sparse signals. In this paper, we adopt…
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…
Signals sparse in a transformation domain can be recovered from a reduced set of randomly positioned samples by using compressive sensing algorithms. Simple re- construction algorithms are presented in the first part of the paper. The…
This paper provides new error bounds on "consistent" reconstruction methods for signals observed from quantized random projections. Those signal estimation techniques guarantee a perfect matching between the available quantized data and a…
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…
In this paper, we investigate the theoretical guarantees of penalized $\lun$ minimization (also called Basis Pursuit Denoising or Lasso) in terms of sparsity pattern recovery (support and sign consistency) from noisy measurements with…
The sparsity in levels model recently inspired a new generation of effective acquisition and reconstruction modalities for compressive imaging. Moreover, it naturally arises in various areas of signal processing such as parallel…
Conventional sparse phase retrieval schemes can recover sparse signals from the magnitude of linear measurements only up to a global phase ambiguity. This work proposes a novel approach that instead utilizes the magnitude of affine…
The choice of the sensing matrix is crucial in compressed sensing. Random Gaussian sensing matrices satisfy the restricted isometry property, which is crucial for solving the sparse recovery problem using convex optimization techniques.…
Sparse recovery aims to reconstruct an unknown spare or approximately sparse signal from significantly few noisy incoherent linear measurements. As a kind of computable incoherence measure of the measurement matrix, $q$-ratio constrained…
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…
This paper studies the problem of recovering a non-negative sparse signal $\x \in \Re^n$ from highly corrupted linear measurements $\y = A\x + \e \in \Re^m$, where $\e$ is an unknown error vector whose nonzero entries may be unbounded.…
Compressive sensing (CS) is a technique for estimating a sparse signal from the random measurements and the measurement matrix. Traditional sparse signal recovery methods have seriously degeneration with the measurement matrix uncertainty…
The recovery of signals that are sparse not in a basis, but rather sparse with respect to an over-complete dictionary is one of the most flexible settings in the field of compressed sensing with numerous applications. As in the standard…
In this paper, {the goal is to design deterministic sampling patterns on the sphere and the rotation group} and, thereby, construct sensing matrices for sparse recovery of band-limited functions. It is first shown that random sensing…
The recovery of Dirac impulses, or spikes, from filtered measurements is a classical problem in signal processing. As the spikes lie in the continuous domain while measurements are discrete, this task is known as super-resolution or…
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,…
In this paper, we present coherence-based performance guarantees of Orthogonal Matching Pursuit (OMP) for both support recovery and signal reconstruction of sparse signals when the measurements are corrupted by noise. In particular, two…
Compressive Sensing (CS) exploits the surprising fact that the information contained in a sparse signal can be preserved in a small number of compressive, often random linear measurements of that signal. Strong theoretical guarantees have…