Publications

Synthetic Aperture Radar systems are being driven to provide images with ever-finer resolutions. This, of course, requires ever-wider bandwidths to support these resolutions in a number of frequency bands across the microwave (and lower) spectrum. The problem is that the spectrum is already quite crowded with a multitude of users, and a multitude of uses. For a radar system, this manifests itself as a number of 'stay-out' zones in the spectrum mandated by regulatory agencies; frequencies where the radar is not allowed to transmit. Even frequencies where the radar is allowed to transmit might be corrupted by interference from other legitimate (and/or illegitimate) users, rendering these frequencies useless to the radar system. In a SAR image, these spectral holes (by whatever source) degrade images, most notably by increasing objectionable sidelobe levels, most evident in the neighborhood of bright point-like objects. For contiguous spectrums, sidelobes in SAR images are controlled by employing window functions. However, those windows that work well for contiguous spectrums don't seem to work well for spectrums with significant gaps or holes. In this paper we address the question "Can some sorts of window functions be developed and employed to advantage when the spectrum is not contiguous, but contains significant holes or gaps?" A window function that minimizes sidelobe energy can be constructed based on prolate spheroidal wave functions. This approach is extended to accommodate spectral notches or holes, although the guaranteed minimum sidelobe energy can be quite high in this case.

Imaging systems such as Synthetic Aperture Radar collect band-limited data from which an image of a target scene is rendered. The band-limited nature of the data generates sidelobes, or ''spilled energy'' most evident in the neighborhood of bright point-like objects. It is generally considered desirable to minimize these sidelobes, even at the expense of some generally small increase in system bandwidth. This is accomplished by shaping the spectrum with window functions prior to inversion or transformation into an image. A window function that minimizes sidelobe energy can be constructed based on prolate spheroidal wave functions. A parametric design procedure allows doing so even with constraints on allowable increases in system bandwidth. This approach is extended to accommodate spectral notches or holes, although the guaranteed minimum sidelobe energy can be quite high in this case. Interestingly, for a fixed bandwidth, the minimum-mean-squared-error image rendering of a target scene is achieved with no windowing at all (rectangular or boxcar window).

Superresolution concepts offer the potential of resolution beyond the classical limit. This great promise has not generally been realized. In this study we investigate the potential application of superresolution concepts to synthetic aperture radar. The analytical basis for superresolution theory is discussed. The application of the concept to synthetic aperture radar is investigated as an operator inversion problem. Generally, the operator inversion problem is ill posed. A criterion for judging superresolution processing of an image is presented.