Fig. 1. Scheme of spectral single-pixel imaging. The target image is modulated by the time-varying patterns uploaded on the DMD. The spectrometer collects the spectral measurements corresponding to each pattern, which are then processed to recover the spectral cube.

Fig. 2. (a) Construction of 1D Hadamard basis vector set V^(k) for k = 2. The corresponding α-index, b_i (Gray code), and index of each v_i in the set are shown below. (b) Construction of 2D Hadamard set P for k = 2. The b_ij of each Hadamard pattern p_ij is shown below each 2D pattern, and the number in parentheses denotes the natural order index I_ij in the index matrix I.

Fig. 3. (a) Morton scanning path to traverse P⁽²⁾. (b) Morton scanning path to traverse index matrix I.

Fig. 4. (a) Original FWHT applied to a vector of length 8^[12]. (b) HFWHT applied to the spectral data matrix Y_M to obtain X. Green lines indicate the elements involved in addition, while red lines indicate those involved in subtraction.

Fig. 5. (a), (b) Plots of MRMSE and MSSIM values with 10% vertical error bars for all 31 spectral cubes from the CAVE dataset. Compared strategies include “Morton,” “Natural,” “Random,” “Cakecutting,” “Data,” and “Zigzag.”

Fig. 6. Comparison of (a) “Zigzag,” (b) “Morton,” (c) “Data,” and (d) “Natural” sampling strategies. Reconstructed pseudo-color images of three spectral cubes at sampling rates of 2%, 10%, and 20% are shown. For each restored image, the MSSIM and MRMSE values are given.

Fig. 7. Experimental setup of the spectral single-pixel imaging system.

Fig. 8. (a) Fused reconstructed pseudo-color images of specific spectral channel. (b) Fused RGB color image under sampling rate of 1%, 2%, 3%, 4%, and 5%. The cube reconstructed using TVAL3 is represented in the first row. The cube reconstructed using HFWHT is shown in the second row.