# Recursive Least Squares for Near-Lossless Hyperspectral Data Compression
###### Abstract  
The hyperspectral image compression scheme is a trade-off between the limited hardware resources of the on-board platform and the ever-growing resolution of the optical instruments. Predictive coding attracts researchers due to its low computational complexity and moderate memory requirements. We propose a near-lossless prediction-based compression scheme that removes spatial and spectral redundant information, thereby significantly reducing the size of hyperspectral images. This scheme predicts the target pixel's value via a linear combination of previous pixels. The weight matrix of the predictor is iteratively updated using a recursive least squares filter with a loop quantizer. The optimal number of bands for prediction was analyzed experimentally. The results indicate that the proposed scheme outperforms state-of-the-art compression methods in terms of the compression ratio and quality retrieval. near-lossless compression; recursive least squares; hyperspectral image; predictive coding +
Footnote †: journal: Applied  
prediction-based subsequent quantization coding, lossless coding based on pre-quantization, and two-stage near-lossless encoding [11]. Predictive-based coding, one of the most popular schemes, enables low-complexity, high-throughput solutions [12; 13; 14]. These schemes first compute the prediction value of the target pixel from the previous encoding. The difference between the predicted and the original pixel value is known as the prediction error. Subsequently, a near-lossless compression scheme is obtained by encoding the quantized prediction error. The two most typical prediction schemes are JPEG-LS [15] and CALIC [16], which are widely used to process two-dimensional images. Meanwhile, the CALIC algorithm, with its better compression performance, is extended to 3D-CALIC [17] and M-CALIC [18] based on the correlation of hyperspectral images. However, the CALIC-based extension scheme cannot effectively remove the redundancy of hyperspectral images and is not friendly to hardware implementation. The Consultative Committee for Space Data Systems (CCSDS) proposes the standard CCSDS-123, which is based on the signed least mean square (SLMS) filter [19; 20]. This compression scheme has low complexity and excellent compression results. NL-CCSDS-123 [10] and CCSDS-123-AC [21] are two near-lossless extended versions that both rely on the predictor of CCSDS-123. The NL-CCSDS-123 scheme encodes the quantized residual pixels after using a range coder, whereas CCSDS-123-AC employs a lightweight context-based arithmetic encoder. However, since their predictor uses a simple function to update the weight coefficients, the prediction accuracy can be further improved. The second type of near-lossless compression category is based on pre-quantizing the original pixels with a quantizer and then applying a lossless compression technique. It is widely known that such a model is suboptimal, and the compression results are not outstanding [22]. However, it is suitable for a scene with high-speed compression demands since it does not need to include a feedback loop. [PERSON] et al. proposed the Pre-CCSDS-IDC [23] compression scheme in order to improve the compression rate without modifying the existing CCSDS-IDC hardware system [24]. It can import the pre-quantized images into CCSDS-IDC directly. In [25] a pre-quantization compression scheme is implemented based on ground-based CNN reconstruction. The spaceborne part can be considered a combination of the pre-quantizer and CCSDS-123 predictor. Eventually, the CNN is employed as a feature extractor on the ground to do a secondary reconstruction of the decoded image, which leads to a higher signal-to-noise ratio. The third near-lossless compression category builds on a combination of lossy and lossless compression. First, the reconstructed images are obtained by lossy compression. Then, the differences between these and the original image are quantized and encoded.