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I would like to extend (cubic or higher degrees) spline wavelets to complex domain. First, does this continuation exist? Second, I appreciate it if anyone could point me to some references.

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An overview with pointers to the literature is Complex B-splines, by Forster, Blu, and Unser; see page 262.

One recent application is Parameter characterization of complex wavelets and its use in 3D reconstruction, by Lopez et al.

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