Algorithmic unfolding for image reconstruction and localization problems in single-molecule fluorescence microscopy

Abstract 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.