Efficient Fourier single-pixel imaging with Gaussian random sampling

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.