Implementation of high‐order variational models made easy for image processing |
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| Authors: | Wenqi Lu Jinming Duan Zhaowen Qiu Zhenkuan Pan Ryan Wen Liu Li Bai |
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| Institution: | 1. College of Information Engineering, Qingdao University, China;2. School of Computer Science, University of Nottingham, UK;3. Institute of Information Computer Engineering, NorthEast Forestry University, China;4. School of Navigation, Wuhan University of Technology, China |
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| Abstract: | High‐order variational models are powerful methods for image processing and analysis, but they can lead to complicated high‐order nonlinear partial differential equations that are difficult to discretise to solve computationally. In this paper, we present some representative high‐order variational models and provide detailed descretisation of these models and numerical implementation of the split Bregman algorithm for solving these models using the fast Fourier transform. We demonstrate the advantages and disadvantages of these high‐order models in the context of image denoising through extensive experiments. The methods and techniques can also be used for other applications, such as image decomposition, inpainting and segmentation. Copyright © 2016 John Wiley & Sons, Ltd. |
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| Keywords: | image processing total variation bounded Hessian total generalised variation total curvature split Bregman algorithm |
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