Difficulties in superresolving synthetic aperture radar images

The ability to resolve Synthetic Aperture Radar (SAR) images to finer resolutions than the system bandwidths classically allow is a tantalizing prospect. Seemingly superresolution offers "something for nothing", or at least "something better than the system was designed for" if only we process 'enough' or 'right'. Over the years this has proved to be a rather popular area of investigation, generating a wide variety of algorithms and corresponding claims of performance. Nevertheless, the literature on the fundamental underlying principles of superresolution as applied to SAR has been rather anemic. This paper addresses the following questions: "What exactly is superresolution?" and "What is not really superresolution, but perhaps more aptly described as image enhancement?" "Is true superresolution possible?" and "to what degree?" "What constrains superresolution?" and very importantly, "How should we objectively test whether an image is in fact superresolved?" Whereas superresolution concepts offer the potential of resolution beyond the classical limit, this great promise has not generally been realized. That is not to say that many reported algorithms have no useful effect on images. True superresolution is defined herein as the 'recovery' of true scene spectrum, that allows more accurate scene rendering. The analytical basis for superresolution theory is outlined, and the application to SAR is then investigated as an operator inversion problem, which is generally 'ill posed. Noise inherent in radar data tends to severely inhibit significant enhancement of image resolution. A criterion for judging superresolution processing of an image is presented.