Fig. 1. Procedure of the proposed method. The light intensity values are collected by the single-pixel detector when the Fourier basis patterns decode with the object. Then the Fourier spectral coefficients are obtained using Eq. (6). Finally, IFT is performed on the spectral coefficients to obtain the reconstructed image.

Fig. 2. Reconstruction results for the Cameraman image using gray Fourier basis patterns under the noise-free condition.

Fig. 3. Reconstruction results for the Cameraman image using binary Fourier basis patterns under the noise-free condition.

Fig. 4. Reconstruction results for the Cameraman image by different methods at different sampling rates under the noise condition.

Fig. 5. Reconstruction results for the Cameraman image by different methods under different Gaussian noise levels.

Fig. 6. Schematic of the experimental system of the proposed method. A white LED illuminates the target, the Fourier basis patterns loaded on the DMD encode the target, then the detector collects the light intensity signals, and the computer reconstructs the image.

Fig. 7. Reconstructed images using strong light by four-step FSPI, three-step FSPI, two-step FSPI, and our method at sampling rates of 5%, 10%, 20%, and 30%.

Fig. 8. Reconstructed images using weak light by four-step FSPI, three-step FSPI, two-step FSPI, and our method at sampling rates of 5%, 10%, 20%, and 30%.