Regularization by architecture: A deep prior approach for inverse problems

Abstract

The present paper studies so-called deep image prior (DIP) techniques in the context of ill-posed inverse problems. DIP networks have been recently introduced for applications in image processing; also first experimental results for applying DIP to inverse problems have been reported. This paper aims at discussing different interpretations of DIP and to obtain analytic results for specific network designs and linear operators. The main contribution is to introduce the idea of viewing these approaches as the optimization of Tikhonov functionals rather than optimizing networks. Besides theoretical results, we present numerical verifications.

References in corpus (5)

• Deep Convolutional Neural Network for Inverse Problems in Imaging
• Learned Primal-dual Reconstruction
• Model based learning for accelerated, limited-view 3D photoacoustic tomography
• Learning Proximal Operators: Using Denoising Networks for Regularizing Inverse Imaging Problems
• Neural Simpletrons - Minimalistic Directed Generative Networks for Learning with Few Labels

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