  The gravitational coupling of a long-wavelength tidal field with small-scale
density fluctuations leads to anisotropic distortions of the locally measured
small-scale matter correlation function. Since the local correlation function
is known to be statistically isotropic in the absence of such tidal
interactions, the tidal distortions can be used to reconstruct the
long-wavelength tidal field and large-scale density field in analogy with the
cosmic microwave background lensing reconstruction. In this paper we present
the theoretical framework of cosmic tidal reconstruction and test the
reconstruction in numerical simulations. We find that the density field on
large scales can be reconstructed with good accuracy and the cross-correlation
coefficient between the reconstructed density field and the original density
field is greater than 0.9 on large scales $(k\lesssim0.1\ h/\mathrm{Mpc})$,
with the filter scale $\sim1.25\ \mathrm{Mpc}/h$. This is useful in the 21cm
intensity mapping survey, where the long-wavelength radial modes are lost due
to a foreground subtraction process.
