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Remotely sensed hyperspectral imagery has vast data volume, for which data compression is a necessary processing step. Spectral decorrelation is critical to successful hyperspectral-image compression. Principal component analysis (PCA) is well-known for its superior performance in data decorrelation, and it has been demonstrated that using PCA for spectral decorrelation can yield rate-distortion and data-analysis performance superior to other widely used approaches, such as the discrete wavelet transform (DWT). However, PCA is a data-dependent transform, and its complicated implementation in hardware hinders its use in practice. In this paper, schemes for low-complexity PCA are discussed, including spatial down-sampling, the use of non-zero mean data, and the adoption of a simple PCA neural-network. System-design issues are also investigated. Experimental results focused on the fidelity of pixel values and pixel spectral signatures demonstrate that the proposed schemes achieve a trade-off between compression performance and system-design complexity.