The image denoising model based on anisotropic diffusion equation often appears the staircase effect while image denoising, and the traditional super-resolution reconstruction algorithm can not effectively suppress the noise in the image in the case of blur and serious noise. To tackle this problem, a novel model is proposed in this paper. Based on the original diffusion equation, we propose a new method for calculating the adaptive fidelity term and its coefficients, which is based on the relationship between the image gradient and the diffusion function. It is realized that the diffusion speed can be slowed down by adaptively changing the coefficient of the fidelity term, and it is proved mathematically that the proposed fractional adaptive fidelity term will not change the existence and uniqueness of the solution of the original model. At the same time, washout filter is introduced as the control item of the model, and a new model of image super-resolution reconstruction and image denoising is constructed. In the proposed model, the order of fractional differential will be determined adaptively by the local variance of the image. And we give the numerical calculation method of the new model in the frequency domain by the method of Fourier transform. The experimental results show that the proposed algorithm can better prevent the staircase effect and achieve better visual effect. And by introducing washout filter to act as the control of the model, the stability of the system can be improved and the system can converge to a stable state quickly.
Citation: Jimin Yu, Jiajun Yin, Shangbo Zhou, Saiao Huang, Xianzhong Xie. An image super-resolution reconstruction model based on fractional-order anisotropic diffusion equation[J]. Mathematical Biosciences and Engineering, 2021, 18(5): 6581-6607. doi: 10.3934/mbe.2021326
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The image denoising model based on anisotropic diffusion equation often appears the staircase effect while image denoising, and the traditional super-resolution reconstruction algorithm can not effectively suppress the noise in the image in the case of blur and serious noise. To tackle this problem, a novel model is proposed in this paper. Based on the original diffusion equation, we propose a new method for calculating the adaptive fidelity term and its coefficients, which is based on the relationship between the image gradient and the diffusion function. It is realized that the diffusion speed can be slowed down by adaptively changing the coefficient of the fidelity term, and it is proved mathematically that the proposed fractional adaptive fidelity term will not change the existence and uniqueness of the solution of the original model. At the same time, washout filter is introduced as the control item of the model, and a new model of image super-resolution reconstruction and image denoising is constructed. In the proposed model, the order of fractional differential will be determined adaptively by the local variance of the image. And we give the numerical calculation method of the new model in the frequency domain by the method of Fourier transform. The experimental results show that the proposed algorithm can better prevent the staircase effect and achieve better visual effect. And by introducing washout filter to act as the control of the model, the stability of the system can be improved and the system can converge to a stable state quickly.
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Jimin Yu, Jiajun Yin, Shangbo Zhou, Saiao Huang, Xianzhong Xie. An image super-resolution reconstruction model based on fractional-order anisotropic diffusion equation[J]. Mathematical Biosciences and Engineering, 2021, 18(5): 6581-6607. doi: 10.3934/mbe.2021326
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