Fourier Spectrum Retrieval in Single-Pixel Imaging

Fourier spectrum represents objects in the frequency domain. Low-frequency coefficients show outlines of objects, and high-frequency coefficients display details of objects. In this paper, we propose a novel and high-efficiency Fourier spectrum retrieval method in single-pixel imaging. First, a small percentage of low-frequency coefficients is measured based on the Fourier spectrum acquisition method. Then, high-frequency coefficients, which are not measured directly, are quickly and efficiently estimated by using the proposed method. In comparison with the conventional Fourier spectrum acquisition method, conventional correlation algorithm and conventional Gerchberg-Saxton-like algorithm, the proposed method shows great advantages in measurement efficiency, since the proposed method can obtain reconstructed objects with high signal-to-noise ratio by using far fewer measurements. In addition, the proposed method also shows its capability in reconstructing high-quality objects under noise contamination. The numerical results and discussion are presented to illustrate feasibility and effectiveness of the proposed method.