Image Restoration Technology Based On Variation Of PDE And Kernel Function

In the process of image acquisition, transmission, and display, the presence of image degradation, such as noise and blurring, is unavoidable. Image restoration refers to restoring the clear and high-quality image from the degenerative one. It is the basis of image processing and pattern recognition, and it plays an important role in astronomy, remote sensing, military imaging, medical imaging, etc. So, image restoration has always been a focus of concern.The traditional methods of image restoration rest on the image filter. Since most of the detailed information is contained in the edges of the image, image filter is required to deblur the image and suppress the noise, while at the same time preserve the details in the edges. However, detailed information and noise are both high frequency parts of the image, which lead to a contradiction between the image smoothing and detailed information preserving during image restoration. The traditional methods of image filter can not deal with such a problem. In recent years, some image processing techniques, such as variational PDE (Partial Differential Equations) method, are emerging to solve this contradiction. Our work is carried out based on this variational PDE method.To pave the way for the rest of the paper in theory, firstly, we introduce some basic knowledge about image restoration and related mathematics. Secondly, the establishment process of the classical total variation is derived in detail and experiment results show the advantage of the classical total variation method. On the basis of this, two image restoration algorithms are proposed, that is, single-channel image blind restoration algorithm and multi-channel image blind restoration algorithm. The detailed process of the single-channel image blind restoration algorithm is that the system PSF(Point Spread Function) is estimated by the priori knowledge of the image at first, and then a proper regularization energy function can be constructed, and finally the degenerative image is restored by minimizing the energy function. To obtain better restoration image, a multi-channel image blind restoration algorithm is proposed by extending the single-channel to multi-channel. Experiment results show that the multi-channel image blind restoration algorithm can effectively remove the blur of the degenerative image, and it has good stability and convergence. However, since the multi-channel image blind restoration algorithm can not suppress the noise sufficiently, the kernel function is introduced to suppress the noise, and finally obtains the desired restoration image.