Compressed sensing (CS) is a new signal processing theory that provides an insight into signal processing. The CS theory has numerous potential applications in various fields, such as image processing, astronomical data analysis, analog-to-information, medical imaging, and remote sensing (RS) imagery. The CS theory is applied to RS video imagery. An RS video based on a compressed sensing (RS-VCS) framework with correlation estimation measurement is proposed, along with a block measurement correlation model and corresponding reconstruction. The linearized Bregman algorithm is used to solve the reconstruction model, and the performance of the RS-VCS framework is simulated numerically.