  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 spherical coordinates. Therefore, the projection of
suitable wavelets defined separably in these coordinates can be computed
analytically, yielding a sequence of wavelets closed under projection. Our
local Fourier slice equation then realizes projection as reconstruction with
"sliced" wavelets 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.
