  Speckle reduction is a key step in many remote sensing applications. By
strongly affecting synthetic aperture radar (SAR) images, it makes them
difficult to analyse. Due to the difficulty to model the spatial correlation of
speckle, a deep learning algorithm with self-supervision is proposed in this
paper: SAR2SAR. Multi-temporal time series are leveraged and the neural network
learns to restore SAR images by only looking at noisy acquisitions. To this
purpose, the recently proposed noise2noise framework has been employed. The
strategy to adapt it to SAR despeckling is presented, based on a compensation
of temporal changes and a loss function adapted to the statistics of speckle.
  A study with synthetic speckle noise is presented to compare the performances
of the proposed method with other state-of-the-art filters. Then, results on
real images are discussed, to show the potential of the proposed algorithm. The
code is made available to allow testing and reproducible research in this
field.
