Reaction–diffusion equation based image restoration

Abstract

We present a novel restoration algorithm based on the reaction–diffusion equation theory, denominated RDER, for restoring images which are corrupted by various blur PSFs and different types of noise (including different levels of impulse noise, Gaussian noise and mixed noise). The focus of this work is to propose an image restoration method based on the reaction diffusion equation and to further extend the traditional diffusion equation. Firstly, the RDER model is constructed by using the restoration ability of the diffusion equation, and the image detail preservation ability of the reaction equation; secondly, based on the difference scheme theory, a discrete RDER model is proposed for image restoration and a RDER algorithm for restoring the image is designed; thirdly, we mathematically analyze the RDER model from the existence, stability and uniqueness of solutions of the RDER model; finally, the proposed RDER algorithm is compared with the current famous state-of-the-art restoration algorithms in image restoring and image details preserving. Theoretical analysis and extensive experimental results show that the RDER is an effective image restoration algorithm for image denoising, image deblurring and image details preserving; in particular, the RDER provides a better performance in terms of the impulse noise and mixed noise.