  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.
