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Constrained energy minimization (CEM) has shown effective in hyperspectral target detection. It linearly constrains a desired target signature while minimizing interfering effects caused by other unknown signatures. This paper explores this idea for band selection and develops a new approach to band selection, referred to as constrained band selection (CBS) for hyperspectral imagery. It interprets a band image as a desired target signature vector while considering other band images as unknown signature vectors. As a result, the proposed CBS using the concept of the CEM to linearly constrain a band image, while also minimizing band correlation or dependence provided by other band images, is referred to as CEM-CBS. Four different criteria referred to as Band Correlation Minimization (BCM), Band Correlation Constraint (BCC), Band Dependence Constraint (BDC), and Band Dependence Minimization (BDM) are derived for CEM-CBS.. Since dimensionality resulting from conversion of a band image to a vector may be huge, the CEM-CBS is further reinterpreted as linearly constrained minimum variance (LCMV)-based CBS by constraining a band image as a matrix where the same four criteria, BCM, BCC, BDC, and BDM, can be also used for LCMV-CBS. In order to determine the number of bands required to select p, a recently developed concept, called virtual dimensionality, is used to estimate the p. Once the p is determined, a set of p desired bands can be selected by the CEM/LCMV-CBS. Finally, experiments are conducted to substantiate the proposed CEM/LCMV-CBS four criteria, BCM, BCC, BDC, and BDM, in comparison with variance-based band selection, information divergence-based band selection, and uniform band selection.