Because of the vast data volume of hyperspectral imagery, compression becomes a necessary process for hyperspectral data transmission, storage, and analysis. Three-dimensional discrete wavelet transform (DWT) based algorithms are particularly of interest due to their excellent rate-distortion performance. This thesis investigates several issues surrounding efficient compression using JPEG2000. Firstly, the rate-distortion performance is studied when Principal Component Analysis (PCA) replaces DWT for spectral decorrelation with the focus on the use of a subset of principal components (PCs) rather than all the PCs. Secondly, the algorithms are evaluated in terms of data analysis performance, such as anomaly detection and linear unmixing, which is directly related to the useful information preserved. Thirdly, the performance of compressing radiance and reflectance data with or without bad band removal is compared, and instructive suggestions are provided for practical applications. Finally, low-complexity PCA algorithms are presented to reduce the computational complexity and facilitate the future hardware design.