Effectiveness of spatially-variant apodization

Sidelobe artifact is a common problem in image reconstruction from finite-extent Fourier data. Conventional shift-invariant windows applied to the Fourier data, reduce sidelobe artifacts at the expense of worsened mainlobe resolution. Stankwitz et al. (1995) have suggested spatially-variant apodization (SVA) as a means of reducing the sidelobe artifacts, while preserving the mainlobe resolution. SVA adaptively selects windows from a set of raised-cosine weighting functions. The algorithm is heuristically motivated, and is known to be effective in synthetic aperture radar (SAR) imaging. However, this technique has received only limited analysis. In this paper, we formulate SVA as a spectral estimator, and show that SVA is a special version of the minimum variance spectral estimator (MVSE). We study the properties of SVA that are inherited from MVSE. Then, we consider the application of SVA to spectral estimation and Fourier reconstruction. Although SVA is effective in SAR, we show that it has limitations for reconstructing real-valued extended targets