*3.2. Heuristic k*2*-Raster*

In this section, we present the results of the experiments using the heuristic *k*2-raster proposed by Ladra et al. [33] on some of our datasets. Table 11 reports results for two hyperspectral scene datasets: AIRS Granule and AVIRIS Uncalibrated Yellowstone. In the experiments, we found that only when *k* = 2 would there be enough repeated sets of codewords in the last level of nodes to help us save space. When *k* ≥ 3, there were no repeated sets of codewords. From the table, it can be seen that there was not much size reduction with *k*<sup>2</sup> *<sup>H</sup>*-raster in most cases. However, if we built a *<sup>k</sup>*2-raster using the best or optimal *k* value, the size was considerably smaller. Therefore, we can see that *k*<sup>2</sup> *<sup>H</sup>*-raster structure did not produce a better size.


**Table 11.** Comparison of the structure size (bpppb) built from *k*2-raster and *k*<sup>2</sup> *<sup>H</sup>*-raster where *k* = 2. The sizes for *k*2-raster using the best *k* value and the optimal *k* value are also shown. The best results are highlighted in blue.

#### *3.3. 3D-2D Mapping*

As discussed earlier, Cruces et al. [34] proposed a 3D to 2D mapping of raster images using *k*2-tree as an alternative to achieve a better compression ratio. We used the *k*2-tree implementation in sdsl-lite software to obtain the sizes for one of our datasets (AG9) from *k* = 2 to *k* = 4. Note that similar to *k*2-raster, if the 2D binary matrix cannot be partitioned into square subquadrants of equal size, it needs to be expanded using Equation (1), and the extra elements are set to zero. The results are presented in Table 12. The sizes for a range of bands from 1481 to 1500 of the scene are also given for comparison.

From the results for AG9, we can see that the 3D-2D mapping did not make the size smaller. Instead, it became larger when the *k* value increased, and therefore, the method did not produce competitive results.
