Image deblur with regularized backward heat diffusion

Image blurring with Gaussian kernel can also be modeled as an heat diffusion partial differential equation (PDE), therefore, image deblur is an inverse problem of PDE. In this paper, we proposed a novel image deblur method: regularized backward heat diffusion (RBHD) PDE, based on inverse problem and PDE theories. We have derived the concrete regularization forms: low-pass filtering or adding high order derivative terms, provided several kinds of RBHD PDE, and analyzed the relationship between the optimal cut-off frequency and the estimated forward diffusion time. Compared to the traditional energy based methods, e.g. Wiener filter, our method is more flexible and extensible, and the experiments shows that RBHD PDE achieves much better results both with and without the exact kernel width, and is more suitable as an experimental blind deblurring method for Gaussian blurry image.