  Super-resolution fluorescence microscopy overcomes blurring arising from
light diffraction, allowing the reconstruction of fine scale details in
biological structures. Standard methods come at the expense of long acquisition
time and/or harmful effects on the biological sample, which makes the problem
quite challenging for the imaging of body cells. A promising new avenue is the
exploitation of molecules fluctuations, allowing live-cell imaging with good
spatio-temporal resolution through common microscopes and conventional
fluorescent dyes. Several numerical algorithms have been developed in the
literature and used for fluctuant time series. These techniques are developed
within the discrete setting, namely the super-resolved image is defined on a
finer grid than the observed images. On the contrary, gridless optimisation
does not rely on a fine grid and is rather an optimisation of Dirac measures in
number, amplitudes and positions. In this work, we present an off-the-grid
problem accounting for the independence of fluctuations.
