Higher-dimensional wavelets and the Douglas-Rachford algorithm

We recast the problem of multiresolution-based wavelet construction in one and higher dimensions as a feasibility problem with constraints which enforce desirable properties such as compact support, smoothness and orthogonality of integer shifts. By employing the Douglas-Rachford algorithm to solve this feasibility problem, we generate one-dimensional and non-separable two-dimensional multiresolution scaling functions and wavelets.