Due to recent technological advances in capturing and processing devices, hyperspectral imaging is becoming available for many commercial and military applications such as remote sensing, surveillance, and forest fire detection. Hyperspectral cameras provide rich information, as they capture each pixel along many frequency bands in the spectrum. The large volume of hyperspectral images as well as their high dimensionality make transmitting them over limited-bandwidth channels a challenge. To address this challenge, we present a method to prioritize the transmission of various components of hyperspectral data based on the application needs, the level of details required, and available bandwidth. This is unlike current works that mostly assume offline processing and the availability of all data beforehand. Our method jointly and optimally selects the spectral bands and their qualities to maximize the utility of the transmitted data. It also enables progressive transmission of hyperspectral data, in which approximate results are obtained with small amount of data and can be refined with additional data. This is a desirable feature for large-scale hyperspectral imaging applications. We have implemented the proposed method and compared it against the state-of-the-art in the literature using hyperspectral imaging datasets. Our experimental results show that the proposed method achieves high accuracy, transmits a small fraction of the hyperspectral data, and significantly outperforms the state-of-the-art; up to 35% improvements in accuracy was achieved.