Structured Signal Models in Compressed Sensing

• Applicant: Dr. Philipp Walk
• Subject Area: Electronic Semiconductors, Components and Circuits, Integrated Systems, Sensor Technology, Theoretical Electrical Engineering
• Term: from 2015 to 2019
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 276005174

Obtaining the information of interest fast and in an efficient manner is certainly one of the main challenges in our information age. The complexity of the objects and systems we study and create grows exponentially in accordance with the famous Moore's law, but at the same time only certain information are of interest for us. Taking this crucial side constraint into account the old rule of Galileo Galilei "measure what can be measured" may have to be replaced by ''measure what should be measured" as pointed out by one of the hosts, whereby the term ''what should" resembles here the fundamental paradigm shift.For more than half a century, the Nyquist sampling rate, given by the inverse of the double band-width W of the signals, was the answer to this question by Shannon, givingthe necessary and sufficient amount of linear measurements needed to identify signals. Nowadays, the information (signals) of interest are not lying in a fixed and known bandwidth anymore but are distributed over a huge area. Such signals can be represented by sparse models, i.e., a union of subspaces where only few of the parameters describing the whole linear space (signal space) are non-zero, but it is not known which of them are non-zero. Instead of sampling the whole bandwidth and selecting the few measurements which are relevant for identification of the signal afterwards, a compressive measurement method which incorporates the sparse representation would be desirable. Indeed such a compressed sensing (CS) method emerged from the work of Candes, Tao, Romberg, and Donoho in 2006, which triggered the above mentioned paradigm shift in sampling theory.The huge success of CS stems hereby not only from a reduced sampling rate but rather from the fact that the reconstruction, which constitutes an NP hard linear inverse problem, is given by the solution of an equivalent convexoptimization problem which can be solved efficiently by linear programs, remains stable for compressible signals, and is robust against noise.In future communications over wireless networks, as in the mobile internet and internet of things (IoT), thecommunication has a very sporadic nature (sparse and asynchronous in time) since the traffic is more and more generated by a machine-to-machine (M2M) communication. Furthermore, in the tactile internet there is a small end-to-end latency of milliseconds which demands very fast and efficient signal processing methods to enable a human-to-machine communication. Since multiple sparsity priors are here acting together in a non-linear fashion, future CS methods have to deal in an efficient and robust way (fast reaction times) with non-linear inverse problems under multiple sparse priors.This will be one of the big challenges in the design of the next generation 5G of cellular mobile devices. Hence, developing advanced CS methods as provided in this project, will be necessary to face these challenges.

• DFG Programme: Research Fellowships
• International Connection: USA
• Hosts: Professor Dr. Babak Hassibi; Dan Romik