Abstract
There are currently two paradigm shifts happening in society and scientific computing: (1) Artificial Intelligence (AI) is replacing humans in problem solving, and, (2) AI is replacing the standard algorithms in computational science and engineering. Since reliable numerical calculations are paramount, algorithms for computational science are traditionally based on two pillars: accuracy and stability. Notably, this is true for image reconstruction, which is a mainstay of computational science, providing fundamental tools in medical, scientific and industrial imaging. In this thesis, we demonstrate that the stability pillar is typically absent in current deep learning and AI-based algorithms for image reconstruction, and we present a solution to why this phenomenon occurs for AI-based methods applied both to image reconstruction and to classification in general. This raises two fundamental questions: how reliable are such algorithms when applied in society, and do AI-based algorithms have the unavoidable Achilles heel of instability? We investigate these phenomena, and we introduce a framework designed to demonstrate, investigate and ultimately answer these fundamental questions.
List of papers
Paper I V. Antun, F. Renna, C. Poon, B. Adcock and A. C. Hansen. ‘On instabilities of deep learning in image reconstruction and the potential costs of AI’. Published in Proceedings of the National Academy of Sciences, 2020. 117 (48), 30088-30095. An author version is included in the thesis. The published version is available at: https://doi.org/10.1073/pnas.1907377117 |
Paper II N. M. Gottschling, V. Antun, B. Adcock and A. C. Hansen. ‘The troublesome kernel: why deep learning for inverse problems is typically unstable’. Submitted for publication in SIAM review. To be published. The paper is removed from the thesis in DUO awaiting publishing. |
Paper III B. Adcock, V. Antun and A. C. Hansen. ‘Uniform recovery in infinite-dimensional compressed sensing and applications to structured binary sampling’. Applied and Computational Harmonic Analysis, 2021. 55, 1-40. An author version is included in the thesis. The published version is available at: https://doi.org/10.1016/j.acha.2021.04.001 |
Paper IV V. Antun and Ø. Ryan. ‘On the unification of schemes for wavelets on the interval’. Acta Applicandae Mathematicae, 2021, 7. An author version is included in the thesis. The published version is available at: https://doi.org/10.1007/s10440-021-00413-6 |
Paper V L. Thesing, V. Antun, A. C. Hansen ‘What do AI algorithms actually learn? – On false structures in deep learning’. arXiv: 1906.01478. To be published. The paper is removed from the thesis in DUO awaiting publishing. |