The characteristics of impulse bursts in remote sensing images are analyzed and a model for this noise is proposed. The model also takes into consideration other noise types, for example, the multiplicative noise present in radar images. As a case study, soft morphological filters utilizing a training-based optimization scheme are used for the noise removal. Different approaches for the training are discussed. It is shown that these techniques can provide an effective removal of impulse bursts. At the same time, other noise types in images, for example, the multiplicative noise, can be suppressed without compromising good edge and detail preservation. Numerical simulation results, as well as examples of real remote sensing images, are presented.