Image restoration and enhancement are important parts of digital image processing, belonging to the early visual image processing problems. Image pre-processing is the necessary preliminary work of image analysis, such as filtering to reduce image noise and to enhance the image edges. The image enhancement technique plays an important role in improving image quality and is good for image post-processing e.g. image segmentation and image tracking. Image restoration and enhancement have been widely used in military, medical, industrial production and other fields. Partial differential equation (PDE) as a sophisticated method of image analysis and processing is of great values of research and application, which needs a deep study. As both the variational model and the anisotropic diffusion model have a complete theoretical framework, a variety of models and sophisticated numerical schemes, introduction of which to the fields of digital image processing and computer vision provides a powerful tool to solve problems undoubtedly . This paper concerns about the applications of the PDE in image restoration and image enhancement. We mainly assay traditional methods of image analysis, study applications of the variational method and diffusion equations in image restoration, as well as their improved algorithm for image enhancement.
Key words: Image restoration, image enhancement, forward and backward diffusion filtering.
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