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Random projections have recently been proposed to enable dimensionality reduction in resource-constrained sensor devices such that the computational burden is shifted to the receiver side of the system in the form of a reconstruction process. While a number compressed-sensing algorithms can provide such reconstruction, the principal-component based compressive-projection principal component analysis (CPPCA) algorithm has been shown to offer better performance for hyperspectral imagery. CPPCA is extended to incorporate both spectral and spatial partitioning of the hyperspectral dataset with experimental results evaluating reconstruction quality not only in terms of squared-error and spectral-angle fidelity but also via performance of the reconstructed data in classification and unmixing tasks. While experimental results demonstrate that either form of partitioning yields significantly better reconstruction than the original, non-partitioned algorithm, CPPCA using both spectral and spatial partitioning together outperforms either of the two used alone.