Related papers: New Bounds for Restricted Isometry Constants
This paper provides performance bounds for compressed sensing in the presence of Poisson noise using expander graphs. The Poisson noise model is appropriate for a variety of applications, including low-light imaging and digital streaming,…
Noiseless compressive sensing is a two-steps setting that allows for undersampling a sparse signal and then reconstructing it without loss of information. The LASSO algorithm, based on $\lone$ regularization, provides an efficient and…
As one of the most plausible convex optimization methods for sparse data reconstruction, $\ell_1$-minimization plays a fundamental role in the development of sparse optimization theory. The stability of this method has been addressed in the…
Dictionary-sparse phase retrieval, which is also known as phase retrieval with redundant dictionary, aims to reconstruct an original dictionary-sparse signal from its measurements without phase information. It is proved that if the…
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…
Explicitly using the block structure of the unknown signal can achieve better reconstruction performance in compressive sensing. Theoretically, an unknown signal with block structure can be accurately recovered from a few number 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…
In compressed sensing, one wishes to acquire an approximately sparse high-dimensional signal $x\in\mathbb{R}^n$ via $m\ll n$ noisy linear measurements, then later approximately recover $x$ given only those measurement outcomes. Various…
Suppose the signal x is realized by driving a k-sparse signal u through an arbitrary unknown stable discrete-linear time invariant system H. These types of processes arise naturally in Reflection Seismology. In this paper we are interested…
In this work, we obtain performance guarantees for modified-CS and for its improved version, modified-CS-Add-LS-Del, for recursive reconstruction of a time sequence of sparse signals from a reduced set of noisy measurements available at…
This paper presents a new analysis for the orthogonal matching pursuit (OMP) algorithm. It is shown that if the restricted isometry property (RIP) is satisfied at sparsity level $O(\bar{k})$, then OMP can recover a $\bar{k}$-sparse signal…
Non-convex constraints have recently proven a valuable tool in many optimisation problems. In particular sparsity constraints have had a significant impact on sampling theory, where they are used in Compressed Sensing and allow structured…
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…
This paper studies the problem of accurately recovering a structured signal from a small number of corrupted sub-Gaussian measurements. We consider three different procedures to reconstruct signal and corruption when different kinds of…
In another related work, U-statistics were used for non-asymptotic "average-case" analysis of random compressed sensing matrices. In this companion paper the same analytical tool is adopted differently - here we perform non-asymptotic…
This paper gives a precise characterization of the fundamental limits of adaptive sensing for diverse estimation and testing problems concerning sparse signals. We consider in particular the setting introduced in (IEEE Trans. Inform. Theory…
In many applications in compressed sensing, the measurement matrix is a Fourier matrix, i.e., it measures the Fourier transform of the underlying signal at some specified `base' frequencies $\{u_i\}_{i=1}^M$, where $M$ is the number of…
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.…
We consider the problem of testing for the presence (or detection) of an unknown sparse signal in additive white noise. Given a fixed measurement budget, much smaller than the dimension of the signal, we consider the general problem of…
The stability of low-rank matrix reconstruction with respect to noise is investigated in this paper. The $\ell_*$-constrained minimal singular value ($\ell_*$-CMSV) of the measurement operator is shown to determine the recovery performance…