Ensio Suonperä ; Tuomo Valkonen - Single-loop methods for bilevel parameter learning in inverse imaging

jnsao:15577 - Journal of Nonsmooth Analysis and Optimization, August 5, 2025, Volume 5 - https://doi.org/10.46298/jnsao-2025-15577
Single-loop methods for bilevel parameter learning in inverse imagingArticle

Authors: Ensio Suonperä ; Tuomo Valkonen

    Bilevel optimisation is used in inverse imaging problems for hyperparameter learning/identification and experimental design, for instance, to find optimal regularisation parameters and forward operators. However, computationally, the process is costly. To reduce this cost, recently so-called single-loop approaches have been introduced. On each step of an outer optimisation method, they take just a single gradient step towards the solution of the inner problem. In this paper, we flexibilise the inner algorithm to include standard methods in inverse imaging. Moreover, as we have recently shown, significant performance improvements can be obtained in PDE-constrained optimisation by interweaving the steps of conventional iterative linear system solvers with the optimisation method. We now demonstrate how the adjoint equation in bilevel problems can also benefit from such interweaving. We evaluate the performance of our approach on identifying the deconvolution kernel for image deblurring, and the subsampling operator for magnetic resonance imaging (MRI).


    Volume: Volume 5
    Section: Original research articles
    Published on: August 5, 2025
    Accepted on: August 1, 2025
    Submitted on: April 25, 2025
    Keywords: Optimization and Control

    Software

    Is supplemented by
    https://doi.org/10.5281/zenodo.15006162
    Suonperä, E., & Valkonen, T. (2025). Codes for "Single-loop methods for bilevel parameter learning in inverse imaging" (Versions 2.0, 1–). Zenodo. 10.5281/ZENODO.15006162

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