  Image restoration is a class of important tasks that emerges from a wide
range of scientific disciplines. It has been noticed that most practical images
can be modeled as a composition from a sparse singularity set (edges) where the
image contents or their gradients change drastically, and cartoon chunks in
which a high degree of regularity is dominant. Enhancing edges while promoting
regularity elsewhere has been an important criterion for successful restoration
in many image classes. In this article, we present a wavelet frame based image
restoration model that captures potential edges and facilitates the restoration
procedure by a dedicated treatment both of singularity and of cartoon.
Moreover, its geometric robustness is enhanced by exploiting subtle inter-scale
information available in the coarse image. To substantiate our intuition, we
prove that this model converges to one variant of the celebrated Mumford-Shah
model when adequate asymptotic specifications are given.
