The course explores the transformative potential of Compressive Sensing (CS) and advanced Electromagnetic Fields Signal Processing (SP) techniques in solving challenging problems in Electromagnetics (EM). These methods, rooted in applied mathematics and data science, provide powerful tools for addressing scenarios where acquiring or processing data is expensive, constrained, or underdetermined—conditions frequently encountered in modern EM applications.

This interdisciplinary course is aimed at equipping participants with:

1. an introduction to the principles of compressive sensing and modern signal processing concepts of interest for EM applications;
2. insight into state-of-the-art algorithmic strategies for sparse reconstruction, low-rank modeling, and information extraction;
3. a broad overview of key applications in electromagnetic theory and engineering, where such techniques have enabled significant performance improvements and new design paradigms.

Theoretical concepts will be complemented with hands-on examples and exercises, emphasizing practical problem-solving in Electromagnetics and showcasing the interplay between mathematical models and physical systems.

Course Topics

• Review of the basics and fundamentals of CP and SP in Electromagnetics
• Compressive sampling: acquisition and retrieval problems, incoherence theory and sparse signal reconstruction
• CP and SP in EM Engineering:
  • Direction-of-arrival estimation and array processing
  • Array synthesis and design
  • Antenna diagnostics from sparse and eventually phaseless data
  • EMC applications
  • Microwave imaging and differential imaging
  • Non destructive testing
  • Radar imaging
  • Wireless channel estimation and sounding techniques for next-gen communications
  • Information theory as applied to Electromagnetics
• Application examples including exercises regarding specific engineering applications of CP and SP methodologies