A New Alternating Minimization Algorithm for Total Variation Image Reconstruction

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 isotropic forms of total variation discretizations. The per-iteration computational complexity of the algorithm is three Fast Fourier Transforms (FFTs). 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 total-variation-based deblurring. Some extensi...

• Type: Journal
• Year: 2008
• Where: SIAMIS
• Authors: Yilun Wang, Junfeng Yang, Wotao Yin, Yin Zhang
• Keywords: Algorithm, Fast Fourier Transform, SIAMIS 2008, Total Variation