Spatially variant apodization for image reconstruction from partial Fourier data

Sidelobe artifacts are a common problem in image reconstruction from finite-extent Fourier data. Conventional shift-invariant windows reduce sidelobe artifacts only at the expense of worsened mainlobe resolution. Spatially variant apodization (SVA) was previously introduced as a means of reducing sidelobe artifacts, while preserving mainlobe resolution. Although the algorithm has been shown to be effective in synthetic aperture radar (SAR), it is heuristically motivated and it has received somewhat limited analysis. In this paper, we show that SVA is a version of minimum-variance spectral estimation (MVSE). We then present a complete development of the four types of two-dimensional SVA for image reconstruction from partial Fourier data. We provide simulation results for various real-valued and complex-valued targets and point out some of the limitations of SVA. Performance measures are presented to help further evaluate the effectiveness of SVA.