# Recursive Least Squares for Near-Lossless Hyperspectral Data Compression
## 3 Experimental Results
### Compression Performance Analysis  
#### 3.2.1 Compression Results  
A total of 16 scene data from three types of hyperspectral image datasets (AC, AU, AIRS) were used as test data sources. The results of CCSDS-123-AC, NILCCSDS-123, and M-CALIC are listed here to compare with the proposed near-lossless compression scheme. Table 2 shows the average compression results for multiple compression schemes at five different peak absolute errors. Table 2 reports compression results in terms of the bit rate. The second column reports the first-order entropy on average (in bit-per-pixel) for each scene type. It represents the  
Figure 3: Average compressed bit-rate for different peak absolute errors: (**a**) encoded at \(\Lambda=0\), (**b**) encoded at \(\Lambda=10\), (**c**) encoded at \(\Lambda=20\), (**d**) encoded at \(\Lambda=30\). entropy of individual pixels, regardless of any correlation among the pixels. In addition, each subsequent column shows the average compression results for a compression scheme at different peak absolute errors \(\Lambda\). The best compression results for each test are indicated in bold. The bracketed text indicates the coding gain of our method relative to other techniques, and a positive difference means our scheme is better. It can be seen that the compression bit rate of each technique decreases rapidly as a function of \(\Lambda\). The reported results indicate that our scheme outperforms the other known schemes for all sensors. For lossless coding (\(\Lambda=0\)), our scheme beats the other schemes by a slight margin. For near-lossless encoding (\(\Lambda>0\)), our scheme provides outstanding compression results; i.e., it clearly yields the lowest ratio of all the compared methods. Compared to CCSDS-123-AC, which has the best-known compression results, on average, the proposal provides benefits ranging from 0.11 to 0.6 bpp, depending on the allowed absolute error of the peak. The previous subsection stated that the computational complexity of NLRLS is \(O(k^{2})\). The computational complexity of the SLMS filter used by CCSDS-123-AC is \(O(k)\), where \(k\) is the number of bands. Although NLRLS has higher complexity than CCSDS-123-AC, it produces better convergence and more accurate predictions. Therefore, the compression results of the NLRLS scheme are better. Graphically, the relative gain of our scheme over CCSDS-123-AC is represented in Figure 4 for different datasets. Each color represents the comparison results using different datasets, and each cluster indicates a different peak absolute error. Therefore, the higher percentage means that our scheme is superior. The results indicate that the proposed scheme provides an average optimization from 5.29% to 31.19% in bit-per-pixel change for different peak absolute errors. The AIRS images, especially, outperform by almost 50% with \(\Lambda\geq 10\). We note that complex image preprocessing can achieve better compression results, such as band reorder, clustering, and super-pixel methods [30; 31]. However, this is beyond the scope of this paper and will not be discussed here.