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This dissertation develops several new algorithms to solve existing problems in practical application of the previously developed PCA+JPEG2000, which has shown superior rate-distortion performance in hyperspectral image compression. In addition, a new scheme is proposed to facilitate multi-temporal hyperspectral image compression. Specifically, the uniqueness in each algorithm is described as follows. 1. An empirical piecewise linear equation is proposed to estimate the optimal number of major principal components (PCs) used in SubPCA+JPEG2000 for AVIRIS data. Sensor-specific equations are presented with excellent fitting performance for AVIRIS, HYDICE, and HyMap data. As a conclusion, a general guideline is provided for finding sensor-specific piecewise linear equations. 2. An anomaly-removal-based hyperspectral image compression algorithm is proposed. It preserves anomalous pixels in a lossless manner, and yields the same or even improved rate-distortion performance. It is particularly useful to SubPCA+JPEG2000 when compressing data with anomalies that may reside in minor PCs. 3. A segmented PCA-based PCA+JPEG2000 compression algorithm is developed, which spectrally partitions an image based on its spectral correlation coefficients. This compression scheme greatly improves the rate-distortion performance of PCA+JPEG2000 when the spatial size of the data is relatively smaller than its spectral size, especially at low bitrates. A sensor-specific partition method is also developed for fast processing with suboptimal performance. 4. A joint multi-temporal image compression scheme is proposed. The algorithm preserves change information in a lossless fashion during the compression. It can yield perfect change detection with slightly degraded rate-distortion performance.