  It is known that if $\Omega \subset \mathbb{R}^{d}$ belongs to a class of
multi-tiling domains when translated by a lattice $\Lambda$, there exists a
Riesz basis of exponentials for $L^{2}(\Omega)$ constructed using $k$
translates of the dual lattice $\Lambda^*$. In this paper, we give an explicit
construction of the corresponding biorthogonal dual Riesz basis. We also extend
the iterative reconstruction algorithm introduced in prior work to this
setting.
