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Fourier single-pixel imaging (FSI) is a branch of single-pixel imaging techniques. It allows any image to be reconstructed by acquiring its Fourier spectrum by using a single-pixel detector. FSI uses Fourier basis patterns for structured illumination or structured detection to acquire the Fourier spectrum of image. However, the spatial resolution of the reconstructed image 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. Consequently, a large number of single-pixel measurements lead to a long data acquisition time, resulting in imaging of a dynamic scene challenging. 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 key to the proposed sampling strategy is to perform a density-varying 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. The final image is reconstructed from the undersampled Fourier spectrum through compressive sensing. We experimentally demonstrate the proposed method is able to reconstruct a sharp and clear image of 256 × 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.

Single-pixel imaging is a novel, to the best of our knowledge, computational imaging scheme, but a large number of measurements are typically required in data acquisition. Full-color single-pixel imaging takes many more measurements than does monochromatic single-pixel imaging. Utilizing the fact that human eyes have a poorer spatial resolution to blues than reds and greens, we propose to sample the blue component of color images with an ultra-low sampling ratio so as to reduce the number of measurements. We demonstrate our method with simulations and experiments, concluding that 95% of the measurements can be reduced in the acquisition of the blue component of natural color images in the size of 256 × 256 pixels, and the resulting images are without remarkable visual loss. Moreover, utilizing the sparsity of natural images, the sampling ratios of the red and green components can be reduced to 15% and 50%, respectively. This Letter may generate a new insight of how to optimize the imaging efficiency by utilizing human vision properties. The proposed method can be adopted by other full-color computational imaging techniques.

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