SAR Image Formation as Wavelet Transform

Abstract

In this paper, we derive the SAR raw data model by applying windowing, sampling and convolution to radar reflectivity. We define the SAR transform as the operation reversing the implicitly performed convolution by inverse convolution applied to SAR raw data. The SAR transform is then compared to both, Fourier and Wavelet transform. In either case, defocusing with a certain waveform is involved. We show that SAR and Fourier transform are two opposite special cases of the Wavelet transform in a slightly generalized sense. Due to the fact that the chirp signal which is generating SAR raw data, formally fulfills all requirements for being a wavelet, we conclude furthermore that there might exist faster SAR processing algorithms than those based on the Fourier transform and discuss the idea towards the goal of fast SAR processing, successively focusing in time domain.