Total Variation Based Methods for Image Restoration

Contacts: Tel: (65)-6516-6250 Office: S14-05-21 Email: [email protected] I mage restoration refers to the process of recovering an ideal image from its corrupted version which is the one we actually observe. The corruptions may be due to noise along the way of acquisition, out-of-focus of the imaging device, or packet loss during transmission of an acquired image from one location to another. There are several components in the restoration of corrupted images. First, we need to specify what an “image” is and what “corrupted” means, i.e., to specify an image model and a degradation model. Next, we need to design a restoration model which reconstructs an image satisfying the image model and reverses the degradation process . Whi le a great deal of research efforts has been dedicated to the design of novel restoration models to solve restoration problems ar isen from new appl icat ions , fundamental image restoration tasks such as denoising, deblurring and inpainting remain the center of focus in developing new paradigms for image restoration. Having said so, there isn’t any major breakthrough in the recent decade in the modeling of the degradation processes of these fundamental tasks . Interestingly, it is some new image models which revolutionize the basic design of restoration models. In this ar t icle, we review a functional analytic point of view to images and show how it leads to some new variational and partial differential equation based restoration models which are more effect ive than previous methods in reconstructing ideal images. Possibly due to its explicit connection to traditional mathematical areas such as partial differential equations, functional analysis, fluid mechanics etc., the area of image restoration attracted researchers across a wide range of areas to join the taskforce. As a result, it is definitely not exaggerate to say that the recent growth of the area of image restoration is tremendously faster than it has been in the past few decades.