We propose an unfolded accelerated projected-gradient descent procedure to estimate model and algorithmic parameters for image super-resolution and molecule localization problems in image 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 detail, a standard ℓ2 cost is considered for image reconstruction (e.g., deconvolution/super-resolution, semi-blind deconvolution) problems, while a smoothed ℓ1 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 synthetic and realistic ISBI data.
@article{arxiv.2403.17506,
title = {Algorithmic unfolding for image reconstruction and localization problems in fluorescence microscopy},
author = {Silvia Bonettini and Luca Calatroni and Danilo Pezzi and Marco Prato},
journal= {arXiv preprint arXiv:2403.17506},
year = {2024}
}