  In biological microscopy, light scattering represents the main limitation to
image at depth. Recently, a set of wavefront shaping techniques has been
developed in order to manipulate coherent light in strongly disordered
materials. The Transmission Matrix approach has shown its capability to inverse
the effect of scattering and efficiently focus light. In practice, the matrix
is usually measured using an invasive detector or low-resolution acoustic guide
stars. Here, we introduce a non-invasive and all-optical strategy based on
linear fluorescence to reconstruct the transmission matrices, to and from a
fluorescent object placed inside a scattering medium. It consists in demixing
the incoherent patterns emitted by the object using low-rank factorizations and
phase retrieval algorithms. We experimentally demonstrate the efficiency of
this method through robust and selective focusing. Additionally, from the same
measurements, it is possible to exploit memory effect correlations to image and
reconstruct extended objects. This approach opens up a new route towards
imaging in scattering media with linear or non-linear contrast mechanisms.
