相关论文: Improved RIP-Based Bounds for Guaranteed Performan…
Compressed sensing (CS) is a signal acquisition paradigm to simultaneously acquire and reduce dimension of signals that admit sparse representations. This is achieved by collecting linear, non-adaptive measurements of a signal, which can be…
Compressed sensing typically deals with the estimation of a system input from its noise-corrupted linear measurements, where the number of measurements is smaller than the number of input components. The performance of the estimation…
This paper considers the exact recovery of $k$-sparse signals in the noiseless setting and support recovery in the noisy case when some prior information on the support of the signals is available. This prior support consists of two parts.…
The simultaneous orthogonal matching pursuit (SOMP) is a popular, greedy approach for common support recovery of a row-sparse matrix. However, compared to the noiseless scenario, the performance analysis of noisy SOMP is still nascent,…
This paper is concerned with the hard thresholding operator which sets all but the $k$ largest absolute elements of a vector to zero. We establish a {\em tight} bound to quantitatively characterize the deviation of the thresholded solution…
In this paper we define a new coherence index, named the global 2-coherence, of a given dictionary and study its relationship with the traditional mutual coherence and the restricted isometry constant. By exploring this relationship, we…
Recent work by Rauhut and Ward developed a notion of weighted sparsity and a corresponding notion of Restricted Isometry Property for the space of weighted sparse signals. Using these notions, we pose a best weighted sparse approximation…
Recently, a tensor-on-tensor (ToT) regression model has been proposed to generalize tensor recovery, encompassing scenarios like scalar-on-tensor regression and tensor-on-vector regression. However, the exponential growth in tensor…
Hard Thresholding Pursuit (HTP) has aroused increasing attention for its robust theoretical guarantees and impressive numerical performance in non-convex optimization. In this paper, we introduce a novel tuning-free procedure, named…
Orthogonal matching pursuit (OMP) is a greedy algorithm widely used for the recovery of sparse signals from compressed measurements. In this paper, we analyze the number of iterations required for the OMP algorithm to perform exact recovery…
Compressed Sensing (CS) is an emerging field that enables reconstruction of a sparse signal $x \in {\mathbb R} ^n$ that has only $k \ll n$ non-zero coefficients from a small number $m \ll n$ of linear projections. The projections are…
We study extensions of compressive sensing and low rank matrix recovery (matrix completion) to the recovery of low rank tensors of higher order from a small number of linear measurements. While the theoretical understanding of low rank…
The purpose of this note is to establish a new generalized Dictionary-Restricted Isometry Property (D-RIP) sparsity bound constant for compressed sensing. For fulfilling D-RIP, the constant $\delta_k$ is used in the definition: $(1…
In phase retrieval, the goal is to recover a complex signal from the magnitude of its linear measurements. While many well-known algorithms guarantee deterministic recovery of the unknown signal using i.i.d. random measurement matrices,…
Inspired by significant real-life applications, in particular, sparse phase retrieval and sparse pulsation frequency detection in Asteroseismology, we investigate a general framework for compressed sensing, where the measurements are…
The restricted isometry constants (RICs) play an important role in exact recovery theory of sparse signals via l_q(0<q<=1) relaxations in compressed sensing. Recently, Cai and Zhang[6] have achieved a sharp bound \delta_tk<\sqrt{1-1/t} for…
Low-rank recovery builds upon ideas from the theory of compressive sensing, which predicts that sparse signals can be accurately reconstructed from incomplete measurements. Iterative thresholding-type algorithms-particularly the normalized…
This paper deals with the computational complexity of conditions which guarantee that the NP-hard problem of finding the sparsest solution to an underdetermined linear system can be solved by efficient algorithms. In the literature, several…
Several exact recovery criteria (ERC) ensuring that orthogonal matching pursuit (OMP) identifies the correct support of sparse signals have been developed in the last few years. These ERC rely on the restricted isometry property (RIP), the…
Recovering a sparse signal from outlier-contaminated measurements is a fundamental challenge in many applications. While existing algorithms predominantly address scenarios with bounded noise or assume known signal sparsity, few methods…