We explore the use of several linear dimensionality reduction techniques that can be easily integrated into the hyperspectral imaging sensor. We investigate their effect on the performance of classical target detection and classification techniques for hyperspectral images. Specifically, each N-dimensional spectral pixel is embedded to an M-dimensional measurement space with M ≪ N by a linear transformation (e.g., random measurement matrices, uniform downsampling, principal component analysis). The detectors/classifiers are then applied to the M-dimensional measurement vectors and their performances are compared to those obtained from the entire N-dimensional spectrum. Through extensive experiments on several hyperspectral imagery data sets, we demonstrate that only a small amount of measurements are necessary to achieve comparable performance to that obtained by exploiting the full N-dimensional pixels.