Introduction to Wave Imaging and Inverse Problems

How do medical scanners see inside the human body, or how do geologists map the earth's crust without digging? The answer lies in the elegant mathematics of wave propagation and inverse problems. This text-based course guides you through the foundational mathematical theories used to reconstruct images from wave data, helping you transition from basic physical principles to modern computational imaging techniques. What you'll learn: - Understand the fundamental physics and mathematics of wave propagation and the wave equation. - Formulate forward and inverse problems to reconstruct hidden structures from wave measurements. - Explore the mathematical principles behind computerized tomography (CT) and Radon transforms. - Analyze how synthetic aperture radar (SAR) and reflection seismology use wave reflection to map environments. - Apply modern regularization techniques to solve ill-posed mathematical inverse problems. - Study computational approaches to imaging, including basic discrete models and optimization algorithms. Starting with core definitions of wave mechanics and signal propagation, the course systematically builds your mathematical toolkit. You will progress through classical transform methods before exploring practical applications in medical, radar, and seismic imaging. This course is designed for beginners in applied mathematics, physics, or engineering who want to understand the theory behind imaging systems. No advanced prior background in imaging science is required, though a basic familiarity with calculus and linear algebra is helpful. Start reading today to unlock the mathematical frameworks that power modern imaging technology.