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SUMMARY:Continuous generative models for inverse problems - Matteo Santace
 saria  (Università degli Studi di Genova)
DTSTART:20230328T151000Z
DTEND:20230328T160000Z
UID:TALK198229@talks.cam.ac.uk
DESCRIPTION:Generative models are a large class of deep learning architect
 ures\, trained to describe a subset of a high dimensional space with a sma
 ll number of parameters. Popular models include variational autoencoders\,
  generative adversarial networks\, normalizing flows and\, more recently\,
  score-based diffusion models. In the context of inverse problems\, genera
 tive models can be used to model prior information on the unknown with a h
 igher level of accuracy than classical regularization methods. In this tal
 k we will present a new data-driven approach to solve inverse problems bas
 ed on generative models. Taking inspiration from well-known convolutional 
 architectures\, we construct and explicitly characterize a class of inject
 ive generative models defined on infinite dimensional functions spaces. Th
 e construction is based on wavelet multi resolution analysis: one of the k
 ey theoretical novelties is the generalization of the strided convolution 
 between discrete signals to an infinite dimensional setting. After an off-
 line training of the generative model\, the proposed reconstruction method
  consists in an iterative scheme in the low-dimensional latent space. The 
 main advantages are the faster iterations and the reduced ill-posedness\, 
 which is shown with new Lipschitz stability estimates. We also present num
 erical simulations validating the theoretical findings for linear and nonl
 inear inverse problems such as electrical impedance tomography. This is jo
 int work in collaboration with G.S. Alberti\, J. Hertrich and S. Sciutto.
LOCATION:Seminar Room 1\, Newton Institute
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