  Light field cameras provide intriguing possibilities, such as post-capture
refocus or the ability to synthesize images from novel viewpoints. This comes,
however, at the price of significant storage requirements. Compression
techniques can be used to reduce these but refocusing and reconstruction
require so far again a dense pixel representation. To avoid this, we introduce
local Fourier slice photography that allows for refocused image reconstruction
directly from a sparse wavelet representation of a light field, either to
obtain an image or a compressed representation of it. The result is made
possible by wavelets that respect the "slicing's" intrinsic structure and
enable us to derive exact reconstruction filters for the refocused image in
closed form. Image reconstruction then amounts to applying these filters to the
light field's wavelet coefficients, and hence no reconstruction of a dense
pixel representation is required. We demonstrate that this substantially
reduces storage requirements and also computation times. We furthermore analyze
the computational complexity of our algorithm and show that it scales linearly
with the size of the reconstructed region and the non-negligible wavelet
coefficients, i.e. with the visual complexity.
