Speaker：Bin Dong(Peking University)
Time：2019-03-07 16:30
Location：Conference Room 117 of Shuli Building at Haiyun Campus
Abstract：Image restoration, including image denoising, deblurring, inpainting, computed tomography, etc., is one of the most important areas in imaging science. In image restoration, wavelet frame based approach PDE based approach (including variational models PDE models) are two of the most successful approaches are widely adopted in both academia industry. The development of the two approaches followed rather different paths: wavelet frame based approach uses the tools from applied harmonic analysis utilize sparsity to model images, while PDE based approach uses functions spaces relies on geometry. Therefore, the two approaches are often considered as different approaches.
The first half of this talk is based on a series of papers, where we established rigorous generic connections between wavelet frame PDE based approach. This includes connections of wavelet frame based approach to total variation model, the Mumford-Shah model, the total generalized variational model. Furthermore, connections of wavelet frame shrinkage to a rather general form of nonlinear evolution PDEs is also established, where the Perona-Malik equation, Osher-Rudin’s shock filters Navier-Stokes image inpainting equation are special cases. Other than the establishment of the links between the two approaches, brnew models for both approaches are also discovered, which combine merits from both approaches, thus outperform existing models in various applications in image restoration.
Our theoretical studies also enable us to connect mathematical modeling computations with deep learning. The connections not only can provide guidance to deep network design, which is a central task in deep learning, but also enable us to tackle challenging problems in applied computation mathematics. In the second half of my talk, I will present our recent work on bridging numerical differential equations with deep neural network design for various tasks of inverse problems, image processing analysis.
