去模糊
算法
全变差去噪
数学
趋同(经济学)
缩小
二次方程
图像复原
计算机科学
图像处理
图像(数学)
数学优化
人工智能
几何学
经济增长
经济
作者
Yilun Wang,Junfeng Yang,Wotao Yin,Yin Zhang
出处
期刊:Siam Journal on Imaging Sciences
[Society for Industrial and Applied Mathematics]
日期:2008-01-01
卷期号:1 (3): 248-272
被引量:1833
摘要
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.
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