A CNN-based computational algorithm for nonlinear image diffusion problem
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A CNN-based computational algorithm for nonlinear image diffusion problem Mahima Lakra1
· Sanjeev Kumar1
Received: 25 September 2019 / Revised: 29 April 2020 / Accepted: 15 May 2020 / © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract In the past, several partial differential equations (PDEs) based methods have been widely studied in image denoising. While solving these methods numerically, some parameters need to be chosen manually. This paper proposes a cellular neural network (CNN) based computational scheme for solving the nonlinear diffusion equation modeled for removing additive noise of digital images. The diffusion acts like smoothing on the noisy image, which is taken as an initial condition for the nonlinear PDE. In the proposed scheme, the template matrices of CNN evolve during the iterative diffusion and act as edge-preserving filters on the noisy images. The evolving diffusion ensures convergence of the diffusion process after a specific diffusion time. Therefore, the advantages of such a CNN-based solution scheme are more accurate restoration in terms of image quality with low computation and memory requirements. The experimental results show the effectiveness of the proposed algorithm on different sets of benchmark images degraded with additive noise. Keywords Additive Gaussian noise · Cellular neural network · Edge preserving filters · Image denoising · Nonlinear diffusion
1 Introduction Image denoising is one of the substantial parts of image processing. Nonlinear diffusion filtering gives an efficient way of designing some popular image denoising algorithms. The partial differential equations (PDEs) of nonlinear diffusion not only remove the additive noise from a degraded image but also preserve the sharp features [30]. All these schemes are considered to solve an inverse problem and, therefore, can be seen as a combination of data fidelity and regularization terms. Several PDE models and their computational schemes exist in the literature. However, these numerical schemes suffer from some limitations, such Mahima Lakra
[email protected] Sanjeev Kumar [email protected] 1
Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, 247667, India
Multimedia Tools and Applications
as stopping criteria of the diffusion iterates, the setting of the diffusion coefficient, and the choice of diffusion coefficient function. Therefore, the existing computation schemes need an embedding of a data-driven procedure to decide the optimal values for some of these parameters from the local image statistics. Despite the existence of a large number of image denoising algorithms, it remains an exciting problem for the image processing community. Several PDEs based models exist in the literature; however, there is a need for data-driven and computationally efficient schemes which terminates the diffusion process to avoid over-smoothing. This work contributes in this direction. Here, we propose a CNN algorithm for solving an advanced nonlinear diffusion model of
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