  On-invasive optical imaging techniques are essential diagnostic tools in many
fields. Although various recent methods have been proposed to utilize and
control light in multiple scattering media, non-invasive optical imaging
through and inside scattering layers across a large field of view remains
elusive due to the physical limits set by the optical memory effect, especially
without wavefront shaping techniques. Here, we demonstrate an approach that
enables non-invasive fluorescence imaging behind scattering layers with
field-of-views extending well beyond the optical memory effect. The method
consists in demixing the speckle patterns emitted by a fluorescent object under
variable unknown random illumination, using matrix factorization and a novel
fingerprint-based reconstruction. Experimental validation shows the efficiency
and robustness of the method with various fluorescent samples, covering a field
of view up to three times the optical memory effect range. Our non-invasive
imaging technique is simple, neither requires a spatial light modulator nor a
guide star, and can be generalized to a wide range of incoherent contrast
mechanisms and illumination schemes.
