**5. Discussion**

With the perspective of HSI application, there are several advantages of using PSP-BS. First, we can observe all the BS results in the whole transmission, where the local BS results (i.e., the BS results in a particular time segment) would not be missed. This is one of the most attractive features in progressive processing [34,35]. For instance, some "weaker bands" would appear during the transmission and disappear later on. Those bands might be very important for analyzing some specific types of ground materials, and should be considered to be selected. Besides, by virtue of progressive processing, the PSP-BS can easily be implemented on specific spatial regions (i.e., sub-image) within the image

scene. Analyzing the partial data is also important. The second advantage of PSP-BS is the saving of storage volume. After PSP-BS is done, the redundant bands can be immediately removed, without waiting to apply the BS algorithm again, which saves time and storage space. The third advantage of PSP-BS is the saving of transmission bandwidth. Once the BS results converge in the early stage of transmission, we can ask the transmitter to re-transmit the rest of the image data only with the selected spectral dimensions, in order to save bandwidth. This is particularly important if the transmission bandwidth is limited, or the volume of original data cube is extremely large.

Similar to PBP, that PSP-BS obeys the principle that the time of processing one band must be less than the time of transmitting one band; in PSP-BS, the processing time at each stage must be less than the time to receive a new spectral pixel. In fact, both PBP and PSP methods suffer from the computation complexity issue when the image size or spectral dimension increases. So a balance between computation capability and transmission bandwidth is a prerequisite for the real-time process. This issue has not been emphasized in the related literature. Unlike the PBP works [33–35], the PSP-OMPBS algorithm is further involved with the iterations related to sequential search. The computing time may increase with the drastic increase of *p*. Thus, the computation time must be further reduced to satisfy the prerequisite. Fortunately, the calculation of PSP-OMPBS can be accelerated by parallel processing. For instance, the task of Step 2, and any terms about matrix multiplication in other steps, can be allocated to different cores of the central processing unit (CPU) to compute. The calculation of the matrix inverse can also be reduced by using a graphics processing unit (GPU). If the processing time cannot be reduced to fulfill the real-time process, we still can perform BS with larger *n* interval. In this case, deriving new recursive equations is necessary. We leave that to our future work.
