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There is increasing interest in dimensionality reduction through random projections due in part to the emerging paradigm of compressed sensing. It is anticipated that signal acquisition with random projections will decrease signal-sensing costs significantly; moreover, it has been demonstrated that both supervised and unsupervised statistical learning algorithms work reliably within randomly projected subspaces. Capitalizing on this latter development, several class-dependent strategies are proposed for the reconstruction of hyperspectral imagery from random projections. In this approach, each hyperspectral pixel is first classified into one of several pixel groups using either a conventional supervised classifier or an unsupervised clustering algorithm. After the grouping procedure, a suitable reconstruction method, such as compressive projection principal component analysis, is employed independently within each group. Experimental results confirm that such class-dependent reconstruction, which employs statistics pertinent to each class as opposed to the global statistics estimated over the entire data set, results in more accurate reconstructions of hyperspectral pixels from random projections.