compressed sensing

A Fixed-Point Continuation Method for l_1-Regularized Minimization with Applications to Compressed Sensing

  • Elaine Hale
  • Wotao Yin
  • Yin Zhang
    • Categories Applications - Science and Engineering, Convex Optimization, Nonsmooth Optimization Tags , , , ,

    We consider solving minimization problems with $\ell_1$-regularization: $$\min \|x\|_1 + \mu f(x),$$ particularly for $f(x) = \frac{1}{2}\|Ax-b\|_M^2$ where $A \in \R^{m \times n}$ with $m < n$. Our goal is to construct efficient and robust algorithms for solving large-scale problems with dense data, and our approach is based on two powerful algorithmic ideas, operator-splitting and ... Read more

    Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization

  • Maryam Fazel
  • Benjamin Recht
  • Pablo A. Parrilo
    • Categories Convex and Nonsmooth Optimization, Semi-definite Programming, Statistics Tags , , ,

    The affine rank minimization problem consists of finding a matrix of minimum rank that satisfies a given system of linear equality constraints. Such problems have appeared in the literature of a diverse set of fields including system identification and control, Euclidean embedding, and collaborative filtering. Although specific instances can often be solved with specialized algorithms, … Read more