An Edge Driven Wavelet Frame Model for Image Restoration

TL;DR

This paper introduces an edge driven wavelet frame model for image restoration that adaptively regularizes smooth and singular regions, improving performance in inpainting and deblurring tasks.

Contribution

The paper presents a novel edge driven wavelet frame model that effectively captures singularities and improves image restoration by differentiating regularization based on image regions.

Findings

Model outperforms existing methods in inpainting and deblurring

Robustness to image approximation and singularity estimation

Provides a rigorous connection between discrete and continuous models

Abstract

Wavelet frame systems are known to be effective in capturing singularities from noisy and degraded images. In this paper, we introduce a new edge driven wavelet frame model for image restoration by approximating images as piecewise smooth functions. With an implicit representation of image singularities sets, the proposed model inflicts different strength of regularization on smooth and singular image regions and edges. The proposed edge driven model is robust to both image approximation and singularity estimation. The implicit formulation also enables an asymptotic analysis of the proposed models and a rigorous connection between the discrete model and a general continuous variational model. Finally, numerical results on image inpainting and deblurring show that the proposed model is compared favorably against several popular image restoration models.