Related papers: Improved RIP-Based Bounds for Guaranteed Performan…

In this letter, we first construct a counter example to show that for any given positive integer $K\geq 2$ and for any $\frac{1}{\sqrt{K+1}}\leq t<1$, there always exist a $K-$sparse $\x$ and a matrix $\A$ with the restricted isometry…

As intelligent reflecting surface (IRS) has emerged as a new and promising technology capable of configuring the wireless environment favorably, channel estimation for IRS-assisted multiple-input multiple-output (MIMO) systems has garnered…

We establish theoretical recovery guarantees of a family of Riemannian optimization algorithms for low rank matrix recovery, which is about recovering an $m\times n$ rank $r$ matrix from $p < mn$ number of linear measurements. The…

Compressed sensing (CS) demonstrates that a sparse, or compressible signal can be acquired using a low rate acquisition process below the Nyquist rate, which projects the signal onto a small set of vectors incoherent with the sparsity…

When the linear measurements of an instance of low-rank matrix recovery satisfy a restricted isometry property (RIP)---i.e. they are approximately norm-preserving---the problem is known to contain no spurious local minima, so exact recovery…

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 restricted isometry property (RIP) is essential for the linear map to guarantee the successful recovery of low-rank matrices. The existing works show that the linear map generated by the measurement matrices with independent and…

The restricted isometry property (RIP) for design matrices gives guarantees for optimal recovery in sparse linear models. It is of high interest in compressed sensing and statistical learning. This property is particularly important for…

The algorithms based on the technique of optimal $k$-thresholding (OT) were recently proposed for signal recovery, and they are very different from the traditional family of hard thresholding methods. However, the computational cost for…

Over the past years, there are increasing interests in recovering the signals from undersampling data where such signals are sparse under some orthogonal dictionary or tight framework, which is referred to be sparse synthetic model. More…

The simulations indicate that the existing hard thresholding technique independent of the residual function may cause a dramatic increase or numerical oscillation of the residual. This inherit drawback of the hard thresholding renders the…

The Kaczmarz method (KZ) and its variants, which are types of stochastic gradient descent (SGD) methods, have been extensively studied due to their simplicity and efficiency in solving linear equation systems. The iterative thresholding…

Compressed sensing is a promising technique that attempts to faithfully recover sparse signal with as few linear and nonadaptive measurements as possible. Its performance is largely determined by the characteristic of sensing matrix.…

Applying the theory of compressive sensing in practice always takes different kinds of perturbations into consideration. In this paper, the recovery performance of greedy pursuits with replacement for sparse recovery is analyzed when both…

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…

We study here sparse recovery problems in the presence of additive noise. We analyze a thresholding version of the CoSaMP algorithm, named Thresholding Greedy Pursuit (TGP). We demonstrate that an appropriate choice of thresholding…

Compressed sensing is a new data acquisition paradigm enabling universal, simple, and reduced-cost acquisition, by exploiting a sparse signal model. Most notably, recovery of the signal by computationally efficient algorithms is guaranteed…

Nonconvex matrix recovery is known to contain no spurious local minima under a restricted isometry property (RIP) with a sufficiently small RIP constant $\delta$. If $\delta$ is too large, however, then counterexamples containing spurious…

Intensively growing approach in signal processing and acquisition, the Compressive Sensing approach, allows sparse signals to be recovered from small number of randomly acquired signal coefficients. This paper analyses some of the commonly…

This paper establishes new restricted isometry conditions for compressed sensing and affine rank minimization. It is shown for compressed sensing that $\delta_{k}^A+\theta_{k,k}^A < 1$ guarantees the exact recovery of all $k$ sparse signals…