Abstract
We propose to learn a data-adaptive convex regularizer, which is parameterized using an input-convex neural network, for variational image reconstruction. The regularizer parameters are learned adversarially by discriminating clean images from the artifact-ridden ones in a training dataset. Convexity of the regularizer is theoretically and practically important since (i) one can establish well-posedness guarantees for the corre- sponding variational reconstruction problem and (ii) devise provably convergent optimization algorithms for reconstruc- tion. In particular, the resulting method is shown to be conver- gent in the sense of regularization and can be solved provably using a gradient-based solver. To demonstrate the performance of our approach for solving inverse problems, we consider de- blurring natural images and reconstruction in X-ray computed tomography (CT) and show that the proposed convex regular- izer is on par with and sometimes superior to state-of-the-art classical and data-driven techniques for inverse problems, es- pecially with severely ill-posed forward operators (such as in limited-angle tomography).
#Create your slides in Markdown - click the Slides button to check out the example.
#Supplementary notes can be added here, including code, math, and images.
Zakhar Shumaylov
Mathematics PhD student at University of Cambridge
My research interests include everything applied mathematics.