Jianwen Huang

A new sufficient condition for non-convex sparse recovery via weighted $\ell_r\!-\!\ell_1$ minimization

  • Jianwen Huang
  • Feng Zhang
    • Categories Data-Mining, Nonsmooth Optimization Tags , , ,

    In this letter, we discuss the reconstruction of sparse signals from undersampled data, which belongs to the core content of compressed sensing. A new sufficient condition in terms of the restricted isometry constant (RIC) and restricted orthogonality constant (ROC) is first established for the performance guarantee of recently proposed non-convex weighted $\ell_r-\ell_1$ minimization in recovering … Read more

    The Null Space Property of the Weighted $\ell_r-\ell_1$ Minimization

  • Jianwen Huang
  • Xinling Liu
    • Categories Data-Mining, Nonsmooth Optimization, Robust Optimization Tags , , ,

    The null space property (NSP), which relies merely on the null space of the sensing matrix column space, has drawn numerous interests in sparse signal recovery. This article studies NSP of the weighted $\ell_r-\ell_1$ minimization. Several versions of NSP of the weighted $\ell_r-\ell_1$ minimization including the weighted $\ell_r-\ell_1$ NSP, the weighted $\ell_r-\ell_1$ stable NSP, the … Read more

    Stable Recovery of Sparse Signals With Non-convex Weighted $r$-Norm Minus $1$-Norm

  • Jianwen Huang
  • Feng Zhang
  • Xinling Liu
  • Jianjun Wang
    • Categories Constrained Nonlinear Optimization, Data-Mining, Nonsmooth Optimization Tags , , ,

    Given the measurement matrix $A$ and the observation signal $y$, the central purpose of compressed sensing is to find the most sparse solution of the underdetermined linear system $y=Ax+z$, where $x$ is the $s$-sparse signal to be recovered and $z$ is the noise vector. Zhou and Yu \cite{Zhou and Yu 2019} recently proposed a novel … Read more

    Analysis non-sparse recovery for non-convex relaxed $\ell_q$ minimization

  • Jianwen Huang
  • Feng Zhang
  • Xinling Liu
  • Jianjun Wang
    • Categories Data-Mining, Nonsmooth Optimization, Unconstrained Optimization Tags , , , ,

    This paper studies construction of signals, which are sparse or nearly sparse with respect to a tight frame $D$ from underdetermined linear systems. In the paper, we propose a non-convex relaxed $\ell_q(0 ArticleDownload View PDF

    The block mutual coherence property condition for signal recovery

  • Wang Hailin
  • Jianjun Wang
  • Jianwen Huang
  • Jia Jinping
  • Feng Zhang
    • Categories Data-Mining, Nonsmooth Optimization, Statistics

    Compressed sensing shows that a sparse signal can stably be recovered from incomplete linear measurements. But, in practical applications, some signals have additional structure, where the nonzero elements arise in some blocks. We call such signals as block-sparse signals. In this paper, the $\ell_2/\ell_1-\alpha\ell_2$ minimization method for the stable recovery of block-sparse signals is investigated. … Read more

    The block mutual coherence property condition for signal recovery

  • Wang Hailin
  • Jianjun Wang
  • Jianwen Huang
  • Feng Zhang
    • Categories Data-Mining, Nonlinear Optimization

    Compressed sensing shows that a sparse signal can stably be recovered from incomplete linear measurements. But, in practical applications, some signals have additional structure, where the nonzero elements arise in some blocks. We call such signals as block-sparse signals. In this paper, the $\ell_2/\ell_1-\alpha\ell_2$ minimization method for the stable recovery of block-sparse signals is investigated. … Read more

    The high-order block RIP for non-convex block-sparse compressed sensing

  • Wang Hailin
  • Jianwen Huang
  • Hou Jinyao
  • Wang Wendong
  • Xinling Liu
  • Feng Zhang
    • Categories Data-Mining, Statistics

    This paper concentrates on the recovery of block-sparse signals, which is not only sparse but also nonzero elements are arrayed into some blocks (clusters) rather than being arbitrary distributed all over the vector, from linear measurements. We establish high-order sufficient conditions based on block RIP to ensure the exact recovery of every block $s$-sparse signal … Read more

    The perturbation analysis of nonconvex low-rank matrix robust recovery

  • Jianjun Wang
  • Jianwen Huang
  • Wang Wendong
  • Feng Zhang
    • Categories Nonsmooth Optimization

    In this paper, we bring forward a completely perturbed nonconvex Schatten $p$-minimization to address a model of completely perturbed low-rank matrix recovery. The paper that based on the restricted isometry property generalizes the investigation to a complete perturbation model thinking over not only noise but also perturbation, gives the restricted isometry property condition that guarantees … Read more

    The perturbation analysis of nonconvex low-rank matrix robust recovery

  • Jianwen Huang
  • Wang Wendong
  • Feng Zhang
    • Categories Applications - Science and Engineering, Data-Mining

    In this paper, we bring forward a completely perturbed nonconvex Schatten $p$-minimization to address a model of completely perturbed low-rank matrix recovery. The paper that based on the restricted isometry property generalizes the investigation to a complete perturbation model thinking over not only noise but also perturbation, gives the restricted isometry property condition that guarantees … Read more

    An analysis of noise folding for low-rank matrix recovery

  • Wang Hailin
  • Jianjun Wang
  • Jianwen Huang
  • Wang Wendong
  • Feng Zhang
    • Categories Approximation Algorithms, Convex Optimization, Data-Mining

    Previous work regarding low-rank matrix recovery has concentrated on the scenarios in which the matrix is noise-free and the measurements are corrupted by noise. However, in practical application, the matrix itself is usually perturbed by random noise preceding to measurement. This paper concisely investigates this scenario and evidences that, for most measurement schemes utilized in … Read more