A New Alternating Minimization Algorithm for Total Variation Image Reconstruction

• DOI: 10.1137/080724265
• Publication Date: 2008-10-29T17:45:01Z
• Authors: Yilun Wang; Junfeng Yang; Wotao Yin; Yin Zhang
• Keywords: Deblurring; Total variation denoising; Minification

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