After re-casting the wavelet construction problem as a feasibility problem with constraints arising from the requirements of compact support, smoothness and orthogonality, the Douglas–Rachford algorithm is employed in the search for multi-dimensional, non-separable, compactly supported, smooth, orthogonal, multiresolution wavelets in the case of translations along the integer lattice and isotropic dyadic dilations. An algorithm for the numerical construction of such wavelets is described. By applying the algorithm, new one-dimensional wavelets are produced as well as genuinely non-separable two-dimensional wavelets.

中文翻译：

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不可分离的多维多分辨率小波：Douglas-Rachford 方法


将小波构造问题重新转化为具有紧支撑、光滑度和正交性要求的约束的可行性问题后，采用 Douglas-Rachford 算法来搜索多维、不可分离、紧支撑、光滑、沿整数晶格平移和各向同性二进膨胀的正交多分辨率小波。描述了这种小波的数值构造的算法。通过应用该算法，可以产生新的一维小波以及真正不可分离的二维小波。