A higher-order variational model for image restoration and its medical applications

Abstract

Image restoration is the most fundamental task in image processing. The goal is to remove or reduce the noise from a given corrupted digital image for improving the performance and accuracy of human or machine vision identifications. Total variation (TV) model, which is a classic model in image restoration, is well-known for reducing noise and recovering sharp edges from a observed noisy image. However, it suffers form the undesired artifacts, such as the staircase effect. To overcome the drawback of the TV model, this thesis proposes a new higher-order regularization for removing noise from synthetic, real, and medical images based on the total curvature regularization. As a result, the associated minimization problem is not appropriate to directly solve by some classical algorithms. We therefore develop a new alternating minimization algorithm. Numerical experiments on synthetic, real and medical images show that the quality of restored images by the proposed method is better than those by the competing models

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