Fig. 1. Spectrum data can be divided into contour and details

Fig. 2. igh and low frequency distribution of corresponding signals when σ is 10，25，250

Fig. 3. Recovery results of different sampling rates under different sparsity constraints (a) Sampling rate: 40%, σ: 10, (b) Sampling rate: 40%, σ: 25, (c) Sampling rate: 40%, σ: 250,(d) Sampling rate: 80%, σ: 10, (e) Sampling rate: 80%, σ: 25, (f) Sampling rate: 80%, σ: 250

Fig. 4. Test results on 500 samples (a) (b): Comparison of recovery accuracy at different sampling rates (σ: 15) ,(c) (d):σ’s impact on recovery accuracy (Sampling rate: 40%)

Fig. 5. Information distribution of carnauba wax spectrum corresponding to different sparse transforms（a）Distribution of different sparse transform coefficients，（b）：Distribution during signal reconstruction at σ=10，（c）Distribution during signal reconstruction at σ=100

Fig. 6. Effect of σ on the recovery results of different sparse decompositions. (a) (b) at a sampling rate of 40%，(c) (d) at a sampling rate of 80%

Fig. 7. Effect of σ on recovery speed of different sparse decompositions. (a) (b) at a sampling rate of 40%，(c) (d) at a sampling rate of 80%

Fig. 8. Laboratory verification equipment and verification results（a）CASSI system，（b）recovered true color image by 80% sampling，（c）PHI imaging results，（d）~（g）Recovered results by two algorithms under 20%，40%，80% and 100%sampling