  When light propagates through opaque material, the spatial information it
holds becomes scrambled, but not necessarily lost. Two classes of techniques
have emerged to recover this information: methods relying on optical memory
effects, and transmission matrix (TM) approaches. Here we develop a general
framework describing the nature of memory effects in structures of arbitrary
geometry. We show how this framework, when combined with wavefront shaping
driven by feedback from a guide-star, enables estimation of the TM of any such
system. This highlights that guide-star assisted imaging is possible regardless
of the type of memory effect a scatterer exhibits. We apply this concept to
multimode fibres (MMFs) and identify a `quasi-radial' memory effect. This
allows the TM of an MMF to be approximated from only one end - an important
step for micro-endoscopy. Our work broadens the applications of memory effects
to a range of novel imaging and optical communication scenarios.
