  Imaging through scattering media is a longstanding issue in a wide range of
applications, including biomedicine, security, and astronomy.
Speckle-correlation imaging is promising for non-invasively seeing through
scattering media by assuming shift-invariance of the scattering process called
the memory effect. However, the memory effect is known to be severely limited
when the medium is thick. Under such a scattering condition,
speckle-correlation imaging is not practical because the correlation of the
speckle decays, reducing the field of view. To address this problem, we present
a method for expanding the field of view of single-shot speckle-correlation
imaging by extrapolating the correlation with a limited memory effect. We
derive the imaging model under this scattering condition and its inversion for
reconstructing the object. Our method simultaneously estimates both the object
and the decay of the speckle correlation based on the gradient descent method.
We numerically and experimentally demonstrate the proposed method by
reconstructing point sources behind scattering media with a limited memory
effect. In the demonstrations, our speckle-correlation imaging method with a
minimal lensless optical setup realized a larger field of view compared with
the conventional one. This study will make techniques for imaging through
scattering media more practical in various fields.
