Wavelet frame systems are known to be effective in capturing singularities from degraded images. In this talk, we introduce a new edge driven wavelet frame model for image restoration by approximating images as piecewise smooth functions. With an implicit representation of singularity sets, the proposed model inflicts different strength of regularization on smooth region and singularities. Our model is robust to both image approximation and singularity estimation. The implicit formulation also enables to provide a rigorous connection between the discrete model and the continuous variational model.

This presentation is part of Minisymposium “MS24 - Data-driven approaches in imaging science (3 parts)”
organized by: Jae Kyu Choi (Institute of Natural Sciences, Shanghai Jiao Tong University) , Chenglong Bao (Yau Mathematical Sciences Center, Tsinghua University) .

Authors:

Jae Kyu Choi (Institute of Natural Sciences, Shanghai Jiao Tong University)

Bin Dong (Peking University)

Xiaoqun Zhang (Institute of Natural Sciences, School of Mathematical Sciences, and MOE-LSC, Shanghai Jiao Tong University)

Keywords:

$\gamma$ convergence, (tight) wavelet frames, edge estimation, framelets, image reconstruction, pointwise convergence, variational method