SAR image construction from periodically gapped phase-history data

It is known that high-resolution synthetic aperture radar (SAR) imaging can be cast as a spectral analysis problem, and consequently a number of sophisticated spectral estimation methods have been applied to SAR imaging. These method include the classical Capon method and the closely related Amplitude and Phase Estimation (APES) algorithm. In this paper, we show how Capon and APES can be extended to deal with spectral analysis of periodically gapped (PG) data, i.e. data where samples are missing in a periodic fashion. This problem is highly relevant for SAR imaging with angular diversity since in that case the measured phase-history data matrix contains missing columns. Our extension of Capon and APES is based on a transform that maps a one-dimensional (1D) periodically gapped time-series into a uniformly sampled two-dimensional (2D) data set. We show that the stationarity properties of the 1D signal are left unchanged by the transformation, and as a result the conventional 2D Capon and APES methods can be applied to the transformed data. An associated inverse transform is used to extract the 1D spectral estimate from the 2D one. The new method is computationally and conceptually non-intricate and it does not involve any interpolation of the missing data. Despite its striking simplicity, numerical results indicate that the new method can be a promising tool for SAR imaging with angular diversity as well as for time-series analysis. In SAR applications, the new method may be particularly suitable for accurate imaging of a small region of interest.

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