**6. Conclusions**

This paper presents an instant BS method based on progressive sample processing (PSP), called PSP-OMPBS. PSP-OMPBS uses a recursive algorithm to efficiently accelerate computation. It processes BS pixel-by-pixel according to the BIS/BIP format, or by re-arranged pixel transmission sequences. Unlike traditional BS methods, which must re-implement the total received data, PSP-OMPBS can immediately obtain BS results when receiving a new pixel by referring to past information. The experiments conducted on two hyperspectral datasets show that PSP-OMPBS can instantly output the BS of each stage with very low computing time. Besides, by adopting different types of pixel transmission sequences, it is proved that using sampled sequences can significantly accelerate the BS convergence speed. Those advantages have allowed PSP-OMPBS to be applied effectively in a real-time manner during pixel transmission, and have potential for real-time BS monitoring. Our future work includes reducing the computational complexity by parallel processing, minimizing the numerical errors, considering other pixel transmission strategies, fusing different BS algorithms with PSP, and extending PSP to other topics in the field of hyperspectral image processing.

**Acknowledgments:** This work was supported by the Ministry of Science and Technology in Grants No.: MOST 105-2221-E-110-085 and MOST 105-2221-E-224-054.

**Author Contributions:** Keng-Hao Liu proposed the idea, derived the theoretical part, designed the experiments, and wrote the paper; Hung-Chang Chien and Meng-Han Lu built the Matlab codes, performed the experiments, and designed the Matlab GUI; Shih-Yu Chen reviewed the paper, inspected the theoretical part, and gave constructive advice.

**Conflicts of Interest:** The authors declare no conflict of interest.
