Ambiguity in Solving Imaging Inverse Problems with Deep-Learning-Based Operators

• Type of Material: Article
• Authors: Davide Evangelista, University of Bologna; Elena Morotti, University of Bologna; Elena Loli Piccolomini, University of Bologna; James Nagy, Emory University
• Language: English
• Date: 2023-07-01
• Publisher: MDPI
• Publication Version: Final Published Version
• Copyright Statement: © 2023 by the authors.
• License: Creative Commons Attribution 4.0 International
• Final Published Version (URL): http://dx.doi.org/10.3390/jimaging9070133
• Title of Journal or Parent Work: JOURNAL OF IMAGING SCIENCE AND TECHNOLOGY
• Volume: 9
• Issue: 7
• Grant/Funding Information: This work was partially supported by the US National Science Foundation, under grants DMS 2038118 and DMS 2208294.
• Keywords: deep learning; inverse problem in imaging; image deblurring; neural networks stability
• Research Categories: Computer Science; Mathematics

Abstract

In recent years, large convolutional neural networks have been widely used as tools for image deblurring, because of their ability in restoring images very precisely. It is well known that image deblurring is mathematically modeled as an ill-posed inverse problem and its solution is difficult to approximate when noise affects the data. Really, one limitation of neural networks for deblurring is their sensitivity to noise and other perturbations, which can lead to instability and produce poor reconstructions. In addition, networks do not necessarily take into account the numerical formulation of the underlying imaging problem when trained end-to-end. In this paper, we propose some strategies to improve stability without losing too much accuracy to deblur images with deep-learning-based methods. First, we suggest a very small neural architecture, which reduces the execution time for training, satisfying a green AI need, and does not extremely amplify noise in the computed image. Second, we introduce a unified framework where a pre-processing step balances the lack of stability of the following neural-network-based step. Two different pre-processors are presented. The former implements a strong parameter-free denoiser, and the latter is a variational-model-based regularized formulation of the latent imaging problem. This framework is also formally characterized by mathematical analysis. Numerical experiments are performed to verify the accuracy and stability of the proposed approaches for image deblurring when unknown or not-quantified noise is present; the results confirm that they improve the network stability with respect to noise. In particular, the model-based framework represents the most reliable trade-off between visual precision and robustness.