  We present a novel Fourier camera, an in-hardware optical compression of
high-speed frames employing pixel-level sign-coded exposure where pixel
intensities temporally modulated as positive and negative exposure are combined
to yield Hadamard coefficients. The orthogonality of Walsh functions ensures
that the noise is not amplified during high-speed frame reconstruction, making
it a much more attractive option for coded exposure systems aimed at very high
frame rate operation. Frame reconstruction is carried out by a single-pass
demosaicking of the spatially multiplexed Walsh functions in a lattice
arrangement, significantly reducing the computational complexity. The
simulation prototype confirms the improved robustness to noise compared to the
binary-coded exposure patterns, such as one-hot encoding and pseudo-random
encoding. Our hardware prototype demonstrated the reconstruction of 4kHz frames
of a moving scene lit by ambient light only.
