Abstract

In this paper we introduce a fractal-based method over (complex-valued) Fourier transforms of functions with compact support \(X \subset \Re\). This method of “iterated Fourier transform systems” (IFTS) has a natural mathematical connection with the fractal-based method of “iterated function systems with greyscale maps” (IFSM) in the spatial domain [6,7]. A major motivation for our formulation is the problem of resolution enhancement of band-limited magnetic resonance images. In an attempt to minimize sampling/transform artifacts, it is our desire to work directly with the raw frequency data provided by an MR imager as much as possible before ‘“returning” to the spatial domain. In this paper, we show that our fractal-based IFTS method can be tailored to perform frequency extrapolation.

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