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.

已知小波帧系统可有效地从嘈杂和降级的图像中捕获奇异点。在本文中，我们通过将图像近似为分段平滑函数，介绍了一种新的边缘驱动小波框架模型，用于图像恢复。利用图像奇异集的隐式表示，所提出的模型在平滑和奇异的图像区域和边缘上施加不同的正则化强度。提出的边缘驱动模型对于图像逼近和奇异性估计均具有鲁棒性。隐式表示法还可以对所提出的模型进行渐进分析，并且可以在离散模型与一般连续变分模型之间建立严格的联系。最后，