Simultaneous Cartoon and Texture Image Restoration with Higher-Order Regularization
Miyoun Jung, Myungjoo Kang · SIAM Journal on Imaging Sciences · 2015
This article introduces a variational color image decomposition and restoration model. The aim is to recover an image from its degraded version, while simultaneously decomposing the image into its cartoon and texture components. The energy involves adaptive higher-order regularizers, incorporated with an edge indicator function. This not only helps cartoon and texture decomposition, but also provides higher quality image restoration by ameliorating the staircasing effect that arises in total variation regularization methods. To realize the proposed models, we present fast and efficient iterative algorithms based on a variable splitting scheme and an augmented Lagrangian method. A convergence analysis of the proposed algorithms is also presented under certain conditions. Numerical results and comparisons demonstrate that the proposed model is more effective than state-of-the-art methods for both image decomposition and restoration.