Fig. 1. Results of 1D signal reconstructed by 1D Mexihat wavelet. (a) (c) 1D sine wave signal and 1D triangle wave signal; (b) (d) results of reconstructing Fig. 1 (a) and Fig. 1 (c) using 1D Mexihat wavelet

Fig. 2. Result of 1D Mexihat wavelet function superposition

Fig. 3. Wavelet function system generated using 1D Mexihat wavelet function on interval length r=4 with two additive phase shifts (n=3) at the zoom scale a=2

Fig. 4. Schematic of illumination pattern generation based on 1D continuous wavelet

Fig. 5. Reconstruction results of different 1D wavelet imaging schemes for 1D signals. (a) Reconstruction results of 1D Mexihat wavelet imaging scheme without semi-continuous wavelet transform; (b) reconstruction results of 1D Gauss wavelet imaging scheme based on semi-continuous wavelet transform; (c) reconstruction results of 1D Mexihat wavelet imaging scheme based on semi-continuous wavelet transform; (d) reconstruction results of 1D Haar wavelet imaging scheme based on semi-continuous wavelet transform

Fig. 6. 1D Mexihat wavelet functions on different interval lengths n

Fig. 7. Simulation imaging results of the ghost imaging scheme based on 1D Mexihat wavelet (n=3) under different defined interval lengths r. (a)-(f) Reconstructed results of 1D Mexihat wavelets under interval lengths r= 0.2, 1, 2, 4, 6, 10

Fig. 8. Simulated imaging results of four illumination pattern ghost imaging schemes in the one-dimensional case. (a) Original image (128×128 pixel size); (b) imaging results of imaging scheme based on 1D Gauss wavelet (r=3.5, n=3); (c) imaging results of imaging scheme based on 1D Mexihat wavelet (r=2.5, n=3); (d) imaging results of imaging scheme based on 1D Haar wavelet; (e) imaging results of imaging scheme based on random binary scatter

Fig. 9. Illumination patterns of the zero-level wavelet functions with 2D Gauss wavelet (n=2)

Fig. 10. Simulated imaging results of four illumination pattern ghost imaging schemes in the 2D case. (a) Original image (128×128 pixel size); (b) imaging results of imaging scheme based on 2D Gauss wavelet (r=3.5, n=2); (c) imaging results of imaging scheme based on 2D Mexihat wavelet (r=3, n=2); (d) imaging results of imaging scheme based on 2D Haar wavelet; (e) imaging results of imaging scheme based on random binary scatter

Fig. 11. Experimental setup of computing ghost imaging

Fig. 12. Experimental imaging results of four illumination pattern ghost imaging schemes in one and two dimensions. (a) Imaging results of imaging scheme based on Gauss wavelet; (b) imaging results of imaging scheme based on Mexihat wavelet; (c) imaging results of imaging scheme based on Haar wavelet; (d) imaging results of imaging scheme based on random binary scatter

Fig. 13. Simulated imaging results of four illumination pattern ghost imaging schemes in one dimension under different noise factors (normalized second-order correlation processing). (a) Imaging results of ghost imaging scheme based on 1D Gauss wavelet pattern (r=3.5, n=3), number of reconstructions is 12285; (b) imaging results of ghost imaging scheme based on 1D Mexihat wavelet pattern (r=2.5, n=3), number of reconstructions is 12285; (c) imaging results of ghost imaging scheme based on 1D Haar wavelet pattern, number of reconstructions is 12288; (d) imaging results of ghost imaging scheme based on random binary scatter pattern, number of reconstructions is 12288

Fig. 14. Simulated imaging results of four illumination pattern ghost imaging schemes in two dimension under different noise factors (normalized second-order correlation processing). (a) Imaging results of ghost imaging scheme based on 2D Gauss wavelet pattern (r=3.5, n=2), number of reconstructions is 16384; (b) imaging results of ghost imaging scheme based on 2D Mexihat wavelet pattern (r=3, n=2), number of reconstructions is 16380; (c) imaging results of ghost imaging scheme based on 2D Haar wavelet pattern, number of reconstructions is 16384; (d) imaging results of ghost imaging scheme based on random binary scatter pattern, number of reconstructions is 16384

Fig. 15. Simulated imaging results of imaging schemes when the light intensity-voltage response of the detector deviates from the linear response. (a) Three different forms of response curves of detector to light intensity; (b) under U=sin(1.7×I), imaging results of the Gauss wavelet pattern, Mexiaht wavelet pattern, and Haar wavelet pattern ghost imaging schemes, respectively, with number of measurements of 12285, 12285, 4096; (c) under U=I2, imaging results of the Gauss wavelet pattern, Mexiaht wavelet pattern, and Haar wavelet pattern ghost imaging schemes, respectively, with number of measurements of 16384,5460,4096