Synthetic aperture radars (SAR) use microwaves to obtain images of the Earth’s surface from airplanes or satellites. SAR images can be taken during nighttime and prove insensitive to the clouds or dust in the atmosphere. Therefore, SAR complements the aerial or spaceborne photography, even though there are fundamental differences between the two technologies. For example, photographs register the intensity of light reflected off the imaged scene, whereas SAR relies on the phase information of radio signals. SAR imaging has a multitude of applications, both military and civilian. The latter range from geosciences to navigation to agriculture and forestry.

In the talk, we will discuss the key aspects of the construction and analysis of mathematical models for SAR imaging. The main concepts include matched filtering, imaging operator, resolution, signal compression, and others. We will see that as in the case of photography, a SAR image will inevitably differ from the original imaged scene even if the conditions of image acquisition are ideal. We will show how to quantify the resulting discrepancies and examine the approaches to their reduction. Then, we will identify the additional difficulties that arise when the conditions of image acquisition are not ideal and discuss the mathematical challenges of their mitigation.

Work supported by the US AFOSR.

Semyon Tsynkov received a MSc degree in Engineering Physics (with concentration in Aerodynamics and Thermodynamics) in 1989 from Moscow Institute for Physics and Technology. He subsequently went on to earn a PhD in Computational Mathematics in 1992 from Russian Academy of Sciences. In 2004, he was awarded a Doctor of Science Degree (Habilitation) in Computational Mathematics, also by Russian Academy of Sciences. Dr Tsynkov joined the Department of Mathematics at NCSU in 2000. Prior to that, he worked as a researcher at NASA Langley Research Center in Hampton, VA, and also taught at Tel Aviv University in Israel. Dr Tsynkov’s work covers a broad range of subjects in applied mathematics, from numerical analysis of partial differential equations to inverse problems in acoustics and electromagnetism. His research has been continuously supported by DoD since 2000.