Advanced Sampling and Retrieval Methods - The Compressive Processing Paradigm

The Compressive Processing (CP) paradigm is fundamentally interdisciplinary, with interplay between applied/pure mathematics and engineering serving to fertilize new researches opening new frontiers. The impact of CP goes far beyond compression and classical signal processing. Whenever acquiring/inverting data/information is difficult, dangerous, or expensive, CP allows to proceed with much less data/information than previously thought possible. Such a possibility has been rapidly exploited in several and different ranges of practical engineering problems almost always leading to striking results that significantly advance the state‐of‐the‐art. The course is targeted to make attendees (i) understanding the basics of CP, (ii) learning the leading-edge and most recent advances on CP-based algorithms, while (iii) overviewing the most appealing applications of CP in advanced engineering fields. Applicative examples including exercises will corroborate the theoretical concepts, as well.

Course topics

• Review of the basics and fundamentals of CP;
• Compressive sampling: acquisition problem and incoherent sampling;
• Compressive sensing: retrieval problem and sparse signal reconstruction;
• Advanced CP-based sampling methodologies at the state-of-the-art;
• Advanced CP-based retrieval methodologies at the state‐of‐the‐art;
• Engineering applications of CP: capabilities, limitations, and perspectives;
• Applicative examples including exercises regarding specific engineering applications of CP sampling and CP retrieval methodologies.

References

1. E. J. Candes and M. B. Wakin, "An introduction to Compressive Sampling," IEEE Signal Proc. Mag., vol. 25, no. 2, pp. 21-30, Mar. 2008.
2. G. Oliveri, M. Salucci, N. Anselmi, and A. Massa, "Compressive sensing as applied to inverse problems for imaging: theory, applications, current trends, and open challenges," IEEE Antennas Propag. Mag., vol. 59, no. 5, pp. 34-46, Oct. 2017.
3. A. Massa, P. Rocca, and G. Oliveri, "Compressive sensing in electromagnetics - A review," IEEE Antennas and Propagation Magazine, pp. 224-238, vol. 57, no. 1, Feb. 2015.