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Adaptive Fourier single pixel imaging based on the radial correlation in the Fourier domain.

Fourier single-pixel imaging (FSI) can directly measure the Fourier coefficients of an object and reconstruct its image, and the technique has attracted attention recently. However, with the current spectrum sampling methods of FSI it is difficult to balance image details and noise suppression within a limited sampling number and a short reconstruction time. To address this problem, the method of adaptive Fourier single-pixel imaging (A-FSI) is proposed to measure the coefficients of the key spectra adaptively. First we examine radial correlation between low-frequency and high-frequency components in the Fourier domain. Based on this correlation, we estimate the positions of significant high-frequency components through the chosen low-frequency components, measure the corresponding Fourier coefficients and form the image. Importantly, the proposed A-FSI only uses the inverse Fourier transform for reconstruction, which is much faster than the algorithm of compressed sensing under the given conditions. Both the simulations and experiments show that the proposed method can keep details of the image and reduce the noise of reconstruction at same time with a limited sampling number and a short reconstruction time. This technology can promote the practical development of single-pixel imaging.