The high dimensionality of hyperspectral imagery challenges image processing and analysis. Band selection is a common technique for dimensionality reduction. When the desired object information is unknown, an unsupervised band selection approach is employed to select the most distinctive and informative bands. Although band selection can significantly alleviate the computational burden in the following data processing and analysis, the process itself may induce additional computation complexity, especially when the image spatial size is large; it may be time-consuming for unsupervised band selection methods that need to take all pixels into consideration. Parallel computing techniques are widely adopted to alleviate the computational burden and to achieve real-time processing of data with vast volume. In this paper, we propose parallel implementations via emerging general-purpose graphics processing units (GPUs) for band selection without changing band selection result. Its speedup performance is comparable to the cluster-based parallel implementation. We also propose an approach to using several selected pixels for unsupervised band selection and the number of pixels needed can be equal to the number of selected bands minus one. With whitened pixel signatures (not the original pixels), band selection performance can be comparable to or even better than that from using all the pixels. For this approach, parallel computing is implemented for pixel selection only, since computational complexity in band selection has been greatly reduced.