A Local Fourier Slice Theorem
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We present a local Fourier slice equation that enables local and sparse projection of a signal. Our result exploits that a slice in frequency space is an iso-parameter set in polar coordinates. The projection of wavelets defined in these coordinates therefore yields a sequence that is closed under projection and with analytically described functions. Our local analogue of the Fourier slice theorem then implements projection as reconstruction with "sliced" wavelets, and with computational costs that scale linearly in the complexity of the projected signal. We numerically evaluate the performance of our local Fourier slice equation for synthetic test data and tomographic reconstruction, demonstrating that locality and sparsity can significantly reduce computation times and memory requirements.
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