  Fourier single-pixel imaging (FSI) is a branch of single-pixel imaging
techniques. It uses Fourier basis patterns as structured patterns for spatial
information acquisition in the Fourier domain. However, the spatial resolution
of the image reconstructed by FSI mainly depends on the number of Fourier
coefficients sampled. The reconstruction of a high-resolution image typically
requires a number of Fourier coefficients to be sampled, and therefore takes a
long data acquisition time. Here we propose a new sampling strategy for FSI. It
allows FSI to reconstruct a clear and sharp image with a reduced number of
measurements. The core of the proposed sampling strategy is to perform a
variable density sampling in the Fourier space and, more importantly, the
density with respect to the importance of Fourier coefficients is subject to a
one-dimensional Gaussian function. Combined with compressive sensing, the
proposed sampling strategy enables better reconstruction quality than
conventional sampling strategies, especially when the sampling ratio is low. We
experimentally demonstrate compressive FSI combined with the proposed sampling
strategy is able to reconstruct a sharp and clear image of 256-by-256 pixels
with a sampling ratio of 10%. The proposed method enables fast single-pixel
imaging and provides a new approach for efficient spatial information
acquisition.
