*4.4. Computing Time*

To validate the real-time capability in BIS/BIP transmission, we first compare three PSP-OMPBSs with the OMPBS performed in a progressive manner. The number of transmitted pixels, *n*, was set from 1 to *N* for each image. The experiments were conducted on a computer with Intel i7-4790 3.6 GHz CPU, 16 GB RAM, Windows 7 and Matlab 2015. The values of computing time are reported by the average of ten random runs.

Figure 12a shows the required computing time of progressive OMPBS, PSP-OMPBS, S-PSP-OMPBS, and B-PSP-OMPBS, implemented on the Pavia dataset, where the *x*-axis presents the *n* value and the *y*-axis presents the corresponding computing time. It can be observed that the computing time of OMPBS significantly increases when *n* increases. This is due to the increase in size of **B**, which results in greater computational complexity for OMPBS. The variation of computing time increases with *n*, too. On the contrary, by virtue of recursive processing, the PSP-BSs produced almost flat curves. The computing time is stably under 0.1 s in most *n* indices. This implies that PSP-BS has the potential to be run in a real-time manner during transmission. Figure 12b–d further shows the individual time curve for PSP-OMPBS, S-PSP-OMPBS, and B-PSP-OMPBS, respectively. It could be seen that the computing times of most of the *n* regions stick on the straight trend line. In those cases, the BS results remained the same, so that the recursive equations could be applied continuously. On the other hand, we can find some of the "peak phenomenon" shown in the curves. Those peaks occurred when the updating condition was not reached. Thus, the optimization problems were solved by non-recursive equations instead. The extra computing time is required.

**Figure 12.** Plots showing the computing time required for different progressive BS methods implemented on the ROSIS Pavia dataset: (**a**) all methods, (**b**) PSP-OMPBS, (**c**) step sequence PSP-OMPBS (S-PSP-OMPBS), and (**d**) block sequence PSP-OMPBS (B-PSP-OMPBS).

Similarly, Figure 13a shows the computing time of progressive OMPBS, PSP-OMPBS, S-PSP-OMPBS, and B-PSP-OMPBS implemented on the Purdue dataset, and Figure 13b–d further shows the individual curves of the three PSP-OMPBSs. Similarly, the three PSP-OMPBS methods required significantly less computing time than OMPBS. The required time for PSP-OMPBSs at is less than 0.07 s from *n* = 1–21,025, while OMPBS needs over 1 s when *n* is larger than 14,000. Again, this implies the superior computational efficiency provided by PSP-OMPBS. Comparing Figure 13 with Figure 12, we can interestingly find that the peak phenomenon occurred more frequently in the Purdue case. This is probably due to the noisy property of the Purdue image. Under the circumstances, the BS result varies easily if the new incoming pixel is a noisy pixel. This results in the instability of BS on the *n*-axis, and thus reduces the opportunity of using recursive equations. Fortunately, the peak phenomenon disappeared gradually after sufficient pixels were received, since in later periods of transmission, the received pixels represented the image well. In other words, the BS results tended to be more stable.

**Figure 13.** *Cont*.

**Figure 13.** Plots of computing time required for different progressive BS methods implemented on the AVIRIS Purdue dataset: (**a**) all methods, (**b**) PSP-BS OMPBS, (**c**) step sequence PSP-OMPBS (S-PSP-OMPBS), and (**d**) block sequence PSP-OMPBS (B-PSP-OMPBS).

It is worth mentioning that PSP-OMPBSs required a little more computing time compared to OMPBS at the beginning of transmission. Figure 14a,b shows the zoom-in computing time plots of the Pavia and Purdue datasets at *n* = 100–1000 and *n* = 100–600. There is a noticeable intersection between the OMPBS and PSP-BS curves at roughly *n* = 300. When *n* is less than 300, PSP-OMPBS requires more computing time because it needs to perform an additional logic operation (i.e., Step 4 in PSP-OMPBS algorithm), which leads to an increase of overall computing time. As *n* grows, the proportion of computing logic operations decreases, and this additional burden is relatively diminished.

**Figure 14.** Zoom-in plots of computing time at the beginning of progressive process: (**a**) the Pavia data, and (**b**) the Purdue data.

Finally, Table 6 lists the overall accumulative computing time of the progressive experiments of Figures 12 and 13. It was found that using PSP-BS could significantly reduce the amount of calculation. In addition, there was no significance difference between three PSP-OMPBS methods.

**Table 6.** The overall required computing time (in seconds) in the experiments.


#### *4.5. Graphical User Intervace Design*

In order to analyze the relationship between the ground location of the received pixels, the produced values of quantitative indexes, and the BS results of progressive processing, a Matlab

graphical user interface (GUI) was developed, as shown in Figure 15. It allows users to load different image data, input *p* values, and choose different PTS methods (original, step, block) with the corresponding parameters. Once all the inputs are loaded and the stage button is pressed, the PSP-OMPBS starts to do real-time BS simulation. The red square in the left will show the image scene, where the red dots present the locations of the received pixels. In the top-right corner, the green square will record the statistics, including the number of received pixels (*n*), the processing time, and ACC value for the current *n*. The time curve of a short period is drawn. In the bottom-right corner, the yellow square shows the BS results of the previous stage and the current stage, in which the red bins denote the instant results of PSP-OMPBS and the black bins denote the BS ground truth.

For an easy illustration, the experiment shown in Figure 15 was performed by B-PSP-OMPBS on the Pavia dataset. The parameters were set by *p* = 10 and *b* = 10. Over time, we can observe that the image gradually filled with red dots (transmitted sample pixels), and the ACC increased until it reached 100%. As a result, the BS can be fully monitored in the whole progressive process.

**Figure 15.** Graphical user interface (GUI) design for PSP-OMPBS.
