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Zbl 1187.68665
Wang, Yilun; Yang, Junfeng; Yin, Wotao; Zhang, Yin
A new alternating minimization algorithm for total variation image reconstruction. (English)
[J] SIAM J. Imaging Sci. 1, No. 3, 248-272, electronic only (2008). ISSN 1936-4954/e

Summary: 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.

MSC 2000:: *68U10 Image processing
65J22 Inverse problems
65K10 Optimization techniques (numerical methods)
65T50 Discrete and fast Fourier transforms
90C25 Convex programming

Keywords: half-quadratic; image deblurring; isotropic total variation; fast Fourier transform

Cited in: Zbl 1206.90245 Zbl 1195.68110 Zbl 1181.68304

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