smooth approximations of nonsmooth functions

A First-Order Smoothed Penalty Method for Compressed Sensing

  • Necdet Serhat Aybat
  • Garud Iyengar
    • Categories Biomedical Applications, Nonsmooth Optimization Tags , , , , ,

    We propose a first-order smoothed penalty algorithm (SPA) to solve the sparse recovery problem min{||x||_1 : Ax=b}. SPA is efficient as long as the matrix-vector product Ax and A^Ty can be computed efficiently; in particular, A need not be an orthogonal projection matrix. SPA converges to the target signal by solving a sequence of penalized … Read more

    NESTA: A Fast and Accurate First-order Method for Sparse Recovery

  • Stephen Becker
  • Jerome Bobin
  • Emmanuel Candès
    • Categories Biomedical Applications, Nonsmooth Optimization, Second-Order Cone Programming Tags , , , , , ,

    Accurate signal recovery or image reconstruction from indirect and possibly under- sampled data is a topic of considerable interest; for example, the literature in the recent field of compressed sensing is already quite immense. Inspired by recent breakthroughs in the development of novel fi rst-order methods in convex optimization, most notably Nesterov’s smoothing technique, this paper … Read more