fast fourier transform

Alternating direction algorithms for total variation deconvolution in image reconstruction

  • Tao Min
  • Junfeng Yang
    • Categories Convex Optimization, Nonsmooth Optimization, Unconstrained Optimization Tags , , , ,

    Image restoration and reconstruction from blurry and noisy observation is known to be ill-posed. To stabilize the recovery, total variation (TV) regularization was introduced by Rudin, Osher and Fatemi in \cite{LIR92}, which has demonstrated superiority in preserving image edges. However, the nondifferentiability of TV makes the underlying optimization problems difficult to solve. In this paper, … Read more

    A fast TVL1-L2 minimization algorithm for signal reconstruction from partial Fourier data

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

    Recent compressive sensing results show that it is possible to accurately reconstruct certain compressible signals from relatively few linear measurements via solving nonsmooth convex ptimization problems. In this paper, we propose a simple and fast algorithm for signal reconstruction from partial Fourier data. The algorithm minimizes the sum of three terms corresponding to total variation, … Read more

    An efficient TVL1 algorithm for deblurring multichannel images corrupted by impulsive noise

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

    We extend a recently proposed alternating minimization algorithm to the case of recovering blurry multichannel (color) images corrupted by impulsive rather than Gaussian noise. The algorithm minimizes the sum of a multichannel extension of total variation (TV), either isotropic or anisotropic, and a data fidelity term measured in the L1-norm. We derive the algorithm by … Read more