Mathematical Challenges for SAR Signal Analysis

Mark Stuff
Michigan Technological University
Michigan Tech Research Institute

An understanding of Fourier transform theory provides much of the mathematical background needed to understand some commonly used SAR processing methods. But some inadequately solved problems in SAR signal processing motivate the study of other mathematical ideas. For example, unknown target motions lead to geometric inverse problems. Consequently, understanding of the geometric information content of radar signals can be gained by proving new theorems in Euclidean geometry, conceived in the spirit of classical invariant theory. From another point of view, some of the geometric problems can be related to the modern topic of the recovery of low rank matrices from sparse observations. Problems in three-dimensional SAR imaging relate to the analogous popular modern topic of sparse solutions of linear systems. Exploitation of three-dimensional information from SAR data raises further questions about the estimation of permutations, and invariants of permutation groups. Also, problems in SAR signal analysis have motivated us to want better understanding of methods for solving variational problems, and numerical issues related to repeated interpolations.

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