A Decoupled method for image inpainting with patch-based low rank regulariztion

In this paper, we propose a decoupled variational method for image inpainting in both image domain and transform domain including wavelet domain and Fourier domain. The original image inpainting problem is decoupled as two minimization problems with different energy functionals. One is image denoising with low rank regularization method, i.e., the patch-based weighted nuclear norm minimization (PWNNM). The other is linear combination in image domain or transform domain. An iterative algorithm is then obtained by minimizing the two problems alternatingly. In particular, we derive the variational formulas for PWNNM and reformulate the denoising process into three steps: image decomposition, patch matrix denoising, and image reconstruction. The convergence of the numerical algorithm is proved under some assumptions. The numerical experiments and comparisons on various images demonstrate the effectiveness of the proposed methods.