  Hyperspectral imaging is an important tool having been applied in various
fields, but still limited in observation of dynamic scenes. In this paper, we
propose a snapshot hyperspectral imaging technique which exploits both spectral
and spatial sparsity of natural scenes. Under the computational imaging scheme,
we conduct spectral dimension reduction and spatial frequency truncation to the
hyperspectral data cube and snapshot it in a low cost manner. Specifically, we
modulate the spectral variations by several broadband spectral filters, and
then map these modulated images into different regions in the Fourier domain.
The encoded image compressed in both spectral and spatial are finally collected
by a monochrome detector. Correspondingly, the reconstruction is essentially a
Fourier domain extraction and spectral dimensional back projection with low
computational load. This Fourier-spectral multiplexing in a 2D sensor
simplifies both the encoding and decoding process, and makes hyperspectral data
captured in a low cost manner. We demonstrate the high performance of our
method by quantitative evaluation on simulation data and build a prototype
system experimentally for further validation.
