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.
Categories: math.CA cs.IT math.IT