$\ell_1hBcminimization

Weak Stability of $\ell_1hBcminimization Methods in Sparse Data Reconstruction

  • H. Jiang
  • Zhi-Quan Luo
  • Yun-Bin Zhao
    • Categories Convex and Nonsmooth Optimization, Data-Mining, Linear Programming Tags , , , , ,

    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 literature under various assumptions such as restricted isometry property (RIP), null space property (NSP), and mutual coherence. In this paper, … Read more

    Alternating Direction Algorithms for $\ell_1hBcProblems in Compressive Sensing

  • Junfeng Yang
  • Yin Zhang
    • Categories Convex and Nonsmooth Optimization, Convex Optimization, Nonsmooth Optimization Tags , , , , ,

    In this paper, we propose and study the use of alternating direction algorithms for several $\ell_1$-norm minimization problems arising from sparse solution recovery in compressive sensing, including the basis pursuit problem, the basis-pursuit denoising problems of both unconstrained and constrained forms, as well as others. We present and investigate two classes of algorithms derived from … Read more