Algorithmic unfolding for image reconstruction and localization problems in single-molecule fluorescence microscopy
We propose an unfolded accelerated projected-gradient descent procedure to estimate model and algorithmic parameters for super-resolution and molecule localization problems in fluorescence microscopy. The variational lower-level constraint enforces sparsity of the solution and encodes different noise statistics (Gaussian, Poisson), while the upper-level cost assesses optimality w.r.t.~the task considered. In more details, a standard $\ell_2$ cost is considered for image reconstruction (e.g., deconvolution/super-resolution, semi-blind deconvolution) problems, while a smoothed $\ell_1$ loss with learned binarization is employed to assess localization precision in some exemplary fluorescence microscopy problems exploiting single-molecule activation. Several numerical experiments are reported to validate the proposed approach on both synthetic and benchmark images from the ISBI datasets.
S. Bonettini, L. Calatroni, D. Pezzi, M. Prato, "Algorithmic unfolding for image reconstruction and localization problems in single-molecule fluorescence microscopy", in IMA Journal of Applied Mathematics, 2026.