Fig. 1. Spectra of different substances. (a) Atmosphere; (b) cloud; (c) aircraft plume; (d) missile plume

Fig. 2. Synthetic infrared images. (a) Infrared background template; (b) synthetic infrared gray background image; (c) synthetic infrared gray image containing target

Fig. 3. Distribution of target and aircraft

Fig. 4. Radiation value of each object at selected bands

Fig. 5. Characteristic multispectral images obtained by fitting

Fig. 6. Sketch map of gray diffusion model

Fig. 7. Algorithm flow chart

Fig. 8. Fuzzy algorithm recognition effect diagrams. (a) Band 1; (b) band 2; (c) band 3, (d) band 4; (e) band 5; (f) integrated band 5

Fig. 9. Spectral angle matching effect. (a) Similarity of 0.92; (b) similarity of 0.98; (c) similarity of 0.99 (missile 1), and 0.9995 (missile 2)