  Synthetic aperture radar (SAR) images are affected by a spatially-correlated
and signal-dependent noise called speckle, which is very severe and may hinder
image exploitation. Despeckling is an important task that aims at removing such
noise, so as to improve the accuracy of all downstream image processing tasks.
The first despeckling methods date back to the 1970's, and several model-based
algorithms have been developed in the subsequent years. The field has received
growing attention, sparkled by the availability of powerful deep learning
models that have yielded excellent performance for inverse problems in image
processing. This paper surveys the literature on deep learning methods applied
to SAR despeckling, covering both the supervised and the more recent
self-supervised approaches. We provide a critical analysis of existing methods
with the objective to recognize the most promising research lines, to identify
the factors that have limited the success of deep models, and to propose ways
forward in an attempt to fully exploit the potential of deep learning for SAR
despeckling.
