2016/09/27 by Jinming Duan, Wil OC Ward, Duan, Jinming +9
Computer Science · Mathematics · Medicine · #Advanced Neuroimaging Techniques and Applications #Computer Vision and Pattern Recognition (cs.CV) #FOS: Computer and information sciences #Medical Image Segmentation Techniques #Tensor decomposition and applications #cs.CV
paper · pdf · doi:10.48550/arxiv.1609.08387
arxiv created 2016/09/27 · openalex publication_date 2016/09/27 · arxiv updated 2016/09/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Second order total variation (SOTV) models have advantages for image reconstruction over their first order counterparts including their ability to remove the staircase artefact in the reconstructed image, but they tend to blur the reconstructed image. To overcome this drawback, we introduce a new Tensor Weighted Second Order (TWSO) model for image reconstruction. Specifically, we develop a novel regulariser for the SOTV model that uses the Frobenius norm of the product of the SOTV Hessian matrix and the anisotropic tensor. We then adapt the alternating direction method of multipliers (ADMM) to solve the proposed model by breaking down the original problem into several subproblems. All the subproblems have closed-forms and can thus be solved efficiently. The proposed method is compared with a range of state-of-the-art approaches such as tensor-based anisotropic diffusion, total generalised variation, Euler's elastica, etc. Numerical experimental results of the method on both synthetic and real images from the Berkeley database BSDS500 demonstrate that the proposed method eliminates both the staircase and blurring effects and outperforms the existing approaches for image inpainting and denoising applications.