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The reconstruction of high-dimensional sparse signals is a challenging task in a wide range of applications. In order to deal with high-dimensional problems, efficient sparse fast Fourier transform algorithms are essential tools. The second and third authors have recently proposed a dimension-incremental approach, which only scales almost linear in the number of required sampling values and almost quadratic in the arithmetic complexity with respect to the spatial dimension d. UsingarXiv:1711.05152v1 fatcat:dsuqwqqhonb2jlggtbmkcm27ui