The general theme running throughout this study is the enhancement of step functions which have been degraded by blur and/or additive noise in some form or another. We deal with step functions in both one and two dimensions. The two main areas of study are i. The enhancement of Synthetic Aperture Radar data. This is data which can be thought of some form of step function in two dimensions, and, ii. The enhancement of one dimensional step functions which have been degraded by both blur and additive noise. Although (i) is very specific to Synthetic Aperture Radar data (ii) is far more general and can be applied to any such data in this general category of steps. In fact a very wide range of problems can be thought of within the general context of being step-related. We describe and develop several methods is this study to deal with such problems.