Super-resolution Methods Based On Nonlinear Diffusion Regularizing Models

Scenes acquired by low-end imaging devices su?er from degradations due to noise and hardware limitations. Many methods and techniques have, therefore, been proposed in the literature to overcome the challenges. Super-resolution, which is an inherently illposed problem, is among the methods that helps to reconstruct high quality scenes from their corresponding degraded versions.Most of the existing super-resolution approaches fail to preserve important image features, such as edges and contours, which provide a better visual appeal to humans.These critical features are also useful in various computer vision applications, such as object detection. In this work, we have proposed some super-resolution methods based on nonlinear di?usion functionals to address the weaknesses of the old methods. The new models have the ability to automatically and adaptively regulate the level of regularization depending upon the local image features. In particular, the proposed methods contain regularizing kernels that are stronger in flat regions and weaker in the neighborhood of the boundaries. This locally adaptive phenomena allow our models to reconstruct sharper and detailed scenes that are relatively free from unnecessary artifacts.Firstly, we have proposed a super-resolution method that is based on the PeronaMalik smoothing functional. The method incorporates a di?usivity component with a spatially varying variable exponent, which automatically changes its value to provide an e?ective regularization. Secondly, a modified version of the Charbonnier model is used to address the super-resolution ill-posedness. This method is flexible and produces appealing super-resolution results as it adapts di?erent regularization models—linear isotropic di?usion, total variation, and Charbonnier—in various regions of the image. Thirdly, we consider the issue of simultaneously enhancing the spatial resolution and restoring the high frequency components of scenes. Therefore, the Papoulis–Gerchberg algorithm has been embedded into the general multiframe super-resolution framework to accomplish the task. Finally, we have derived a new regularizing potential for a super-resolution problem. To ensure convexity, smoothness, and monotonicity of the potential, a condition is imposed into the shape-defining parameter. Our analysis on the potential reveals that it allows the super-resolution model to achieve higher resolutions that are unattainable by most other classical methods.The proposed methods can be extended and applied in a variety of fields. For example, they can be used to improve the quality of blood-smear medical images to accurately detect and diagnose a particular disease. The available techniques for this task demand expensive microscopy devices that may be una?ordable. With the super-resolution technology, however, we can embed the algorithms into the low-end(inexpensive) imaging devices to enhance the quality of the input images while maintaining higher accuracies.Empirical results from both simulated and real scenes demonstrate that our models are superior—higher values of performance indices and visually appealing reconstructed scenes.