Arndt, Clemens; Denker, Alexander; Dittmer, Sören; Heilenkötter, Nick; Iske, Meira; Kluth, Tobias; Maass, Peter; Arndt, Clemens; Denker, Alexander; Dittmer, Sören; Heilenkötter, Nick; Iske, Meira; Kluth, Tobias; Maass, Peter; Nickel, Judith; - view fewer (2023) Invertible residual networks in the context of regularization theory for linear inverse problems. Inverse Problems , 39 (12) , Article 125018. 10.1088/1361-6420/ad0660.

Preview

Text Denker_Arndt_2023_Inverse_Problems_39_125018.pdf Download (1MB) | Preview

Abstract

Learned inverse problem solvers exhibit remarkable performance in applications like image reconstruction tasks. These data-driven reconstruction methods often follow a two-step procedure. First, one trains the often neural network-based reconstruction scheme via a dataset. Second, one applies the scheme to new measurements to obtain reconstructions. We follow these steps but parameterize the reconstruction scheme with invertible residual networks (iResNets). We demonstrate that the invertibility enables investigating the influence of the training and architecture choices on the resulting reconstruction scheme. For example, assuming local approximation properties of the network, we show that these schemes become convergent regularizations. In addition, the investigations reveal a formal link to the linear regularization theory of linear inverse problems and provide a nonlinear spectral regularization for particular architecture classes. On the numerical side, we investigate the local approximation property of selected trained architectures and present a series of experiments on the MNIST dataset that underpin and extend our theoretical findings.

Download activity - last month

Export as JSONXMLCSV

Download activity - last 12 months

Export as JSONCSVXML

Downloads by country - last 12 months

Export as XMLCSVJSON

Archive Staff Only

View Item