相关论文: Analysis of Optimal Thresholding Algorithms for Co…

In this paper we present a new coherence-based performance guarantee for the Orthogonal Matching Pursuit (OMP) algorithm. A lower bound for the probability of correctly identifying the support of a sparse signal with additive white Gaussian…

Highly coherent sensing matrices arise in discretization of continuum imaging problems such as radar and medical imaging when the grid spacing is below the Rayleigh threshold. Algorithms based on techniques of band exclusion (BE) and local…

Simultaneous orthogonal matching pursuit (SOMP) and block OMP (BOMP) are two widely used techniques for sparse support recovery in multiple measurement vector (MMV) and block sparse (BS) models respectively. For optimal performance, both…

We propose a class of greedy algorithms for weighted sparse recovery by considering new loss function-based generalizations of Orthogonal Matching Pursuit (OMP). Given a (regularized) loss function, the proposed algorithms alternate the…

In this paper we present a new coherence-based performance guarantee for the Orthogonal Matching Pursuit (OMP) algorithm. An upper bound for the probability of correctly identifying the support of a sparse signal with additive white…

Compressive sensing has been receiving a great deal of interest from researchers in many areas because of its ability in speeding up data acquisition. This framework allows fast signal acquisition and compression when signals are sparse in…

Optimal transport (OT) naturally arises in a wide range of machine learning applications but may often become the computational bottleneck. Recently, one line of works propose to solve OT approximately by searching the \emph{transport plan}…

Optimizing the acquisition matrix is useful for compressed sensing of signals that are sparse in overcomplete dictionaries, because the acquisition matrix can be adapted to the particular correlations of the dictionary atoms. In this paper…

The idea of compressed sensing is to exploit representations in suitable (overcomplete) dictionaries that allow to recover signals far beyond the Nyquist rate provided that they admit a sparse representation in the respective dictionary.…

Optimal Transport (OT) based distances are powerful tools for machine learning to compare probability measures and manipulate them using OT maps. In this field, a setting of interest is semi-discrete OT, where the source measure $\mu$ is…

In this paper, we analyze the generalization performance of the Iterative Hard Thresholding (IHT) algorithm widely used for sparse recovery problems. The parameter estimation and sparsity recovery consistency of IHT has long been known in…

Highly coherent sensing matrices arise in discretization of continuum problems such as radar and medical imaging when the grid spacing is below the Rayleigh threshold as well as in using highly coherent, redundant dictionaries as…

This paper studies the convergence of the adaptively iterative thresholding (AIT) algorithm for compressed sensing. We first introduce a generalized restricted isometry property (gRIP). Then we prove that the AIT algorithm converges to the…

The one-bit compressed sensing framework aims to reconstruct a sparse signal by only using the sign information of its linear measurements. To compensate for the loss of scale information, past studies in the area have proposed recovering…

In the context of compressed sensing (CS), both Subspace Pursuit (SP) and Compressive Sampling Matching Pursuit (CoSaMP) are very important iterative greedy recovery algorithms which could reduce the recovery complexity greatly comparing…

In this paper, we study the problem of compressed sensing using binary measurement matrices and $\ell_1$-norm minimization (basis pursuit) as the recovery algorithm. We derive new upper and lower bounds on the number of measurements to…

We show that if a matrix $\Phi$ satisfies the RIP of order $[CK^{1.2}]$ with isometry constant $\dt = c K^{-0.2}$ and has coherence less than $1/(20 K^{0.8})$, then Orthogonal Matching Pursuit (OMP) will recover $K$-sparse signal $x$ from…

Compressed indexing is a powerful technique that enables efficient querying over data stored in compressed form, significantly reducing memory usage and often accelerating computation. While extensive progress has been made for…

Radio interferometry has always faced the problem of incomplete sampling of the Fourier plane. A possible remedy can be found in the promising new theory of compressed sensing (CS), which allows for the accurate recovery of sparse signals…

The Sinkhorn--Knopp (SK) algorithm is a cornerstone method for matrix scaling and entropically regularized optimal transport (EOT). Despite its empirical efficiency, existing theoretical guarantees to achieve a target marginal accuracy…