A New Alternating Minimization Algorithm for Total Variation Image Reconstruction

  • Authors:

  • Yilun Wang;Junfeng Yang;Wotao Yin;Yin Zhang

  • Affiliations:

  • yilun.wang@rice.edu and wotao.yin@rice.edu and yzhang@rice.edu;jfyang2992@yahoo.com.cn;-;-

  • Venue:
  • SIAM Journal on Imaging Sciences
  • Year:
  • 2008

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Abstract

We propose, analyze, and test an alternating minimization algorithm for recovering images from blurry and noisy observations with total variation (TV) regularization. This algorithm arises from a new half-quadratic model applicable to not only the anisotropic but also the isotropic forms of TV discretizations. The per-iteration computational complexity of the algorithm is three fast Fourier transforms. We establish strong convergence properties for the algorithm including finite convergence for some variables and relatively fast exponential (or $q$-linear in optimization terminology) convergence for the others. Furthermore, we propose a continuation scheme to accelerate the practical convergence of the algorithm. Extensive numerical results show that our algorithm performs favorably in comparison to several state-of-the-art algorithms. In particular, it runs orders of magnitude faster than the lagged diffusivity algorithm for TV-based deblurring. Some extensions of our algorithm are also discussed.