  Speckle based imaging consists of forming a super-resolved reconstruction of
an unknown sample from low-resolution images obtained under random
inhomogeneous illuminations (speckles). In a blind context where the
illuminations are unknown, we study the intrinsic capacity of speckle-based
imagers to recover spatial frequencies outside the frequency support of the
data, with minimal assumptions about the sample. We demonstrate that, under
physically realistic conditions, the covariance of the data has a
super-resolution power corresponding to the squared magnitude of the imager
point spread function. This theoretical result is important for many practical
imaging systems such as acoustic and electromagnetic tomographs, fluorescence
and photoacoustic microscopes, or synthetic aperture radar imaging. A numerical
validation is presented in the case of fluorescence microscopy.
