The emerging theory of Compressed Sensing (CS), changed the very essence of our thinking about signal recovery, system identification and parameter vector estimation. Since its debut only a few years ago, CS attracted considerable research interest with thousands of papers spanning along the Mathematical, Machine Learning and Signal Processing communities. This ``research happening'' gave birth to many significant contributions bringing the CS paradigm closer to a wide range of real-world applications.The vast amount of efforts, so far, has been invested in CS-based signal recovery techniques, which are appropriate for batch mode operation. This fact poses restrictions and inconveniences in cases, where online / real-time processing is necessary. Indeed, all the online sparsity-aware signal recovery methods, so far, are in a ``primitive'' stage of development compared to the state-of-the-art in CS. There is a reason for this; the extension of batch CS methods to perform online processing is not a straightforward task and both new algorithmic and theoretical tools have to be developed towards this goal.The current proposal takes this challenge, i.e. to develop a generic algorithmic framework for online signal and system recovery, which will embody advanced developments of the CS theory. Moreover, the developed techniques will be of linear complexity, thus being suitable for real-time operation and capable of dealing with multiple-sensor cases and distributed processing, required in wireless sensor networks. The effectiveness of the proposed approach will also be evaluated in a real-world medical application; a wireless multi-channel electrocardiogram monitoring system.This project provides the fellow an excellent opportunity to gain high quality scientific training and complementary skills, necessary to obtain the professional maturity required for an academic career.