  Deep learning (DL) in remote sensing has nowadays become an effective
operative tool: it is largely used in applications such as change detection,
image restoration, segmentation, detection and classification. With reference
to synthetic aperture radar (SAR) domain the application of DL techniques is
not straightforward due to non trivial interpretation of SAR images, specially
caused by the presence of speckle. Several deep learning solutions for SAR
despeckling have been proposed in the last few years. Most of these solutions
focus on the definition of different network architectures with similar cost
functions not involving SAR image properties. In this paper, a convolutional
neural network (CNN) with a multi-objective cost function taking care of
spatial and statistical properties of the SAR image is proposed. This is
achieved by the definition of a peculiar loss function obtained by the weighted
combination of three different terms. Each of this term is dedicated mainly to
one of the following SAR image characteristics: spatial details, speckle
statistical properties and strong scatterers identification. Their combination
allows to balance these effects. Moreover, a specifically designed architecture
is proposed for effectively extract distinctive features within the considered
framework. Experiments on simulated and real SAR images show the accuracy of
the proposed method compared to the State-of-Art despeckling algorithms, both
from quantitative and qualitative point of view. The importance of considering
such SAR properties in the cost function is crucial for a correct noise
rejection and details preservation in different underlined scenarios, such as
homogeneous, heterogeneous and extremely heterogeneous.
