In Wireless Body Area Networks (WBAN) the energy consumption is dominated by sensing, processing and communication. Previous Compressed Sensing (CS) based solutions to EEG tele-monitoring over WBAN's could only reduce the communication cost. In this work, we propose to reduce the sensing and processing energy costs as well, by randomly under-sampling the signal. We formulate a theoretically sound framework based on Kronecker Compressed Sensing (KCS) for recovering signals acquired via random under-sampling. We have shown experimentally that when the signals are acquired via under-sampling, all previous CS based techniques fail; only our proposed formulation succeeds. We have also carried out a discussion on the power savings provided by our method; the analysis indicate significant reduction in energy cost.