  Super-resolution light microscopy overcomes the physical barriers due to
light diffraction, allowing for the observation of otherwise indistinguishable
subcellular entities. However, the specific acquisition conditions required by
state-of-the-art super-resolution methods to achieve adequate spatio-temporal
resolution are often very challenging. Exploiting molecules fluctuations allows
good spatio-temporal resolution live-cell imaging by means of common
microscopes and conventional fluorescent dyes. In this work, we present the
method COL0RME for COvariance-based $\ell_0$ super-Resolution Microscopy with
intensity Estimation. It codifies the assumption of sparse distribution of the
fluorescent molecules as well as the temporal and spatial independence between
emitters via a non-convex optimization problem formulated in the covariance
domain. In order to deal with real data, the proposed approach also estimates
background and noise statistics. It also includes a final estimation step where
intensity information is retrieved, which is valuable for biological
interpretation and future applications to super-resolution imaging.
