In SAR domain many application like classification, detection and segmentation are impaired by speckle. Hence, despeckling of SAR images is the key for scene understanding. Usually despeckling filters face the trade-off of speckle suppression and information preservation. In the last years deep learning solutions for speckle reduction have been proposed. One the biggest issue for these methods is how to train a network given the lack of a reference. In this work we proposed a convolutional neural network based solution trained on simulated data. We propose the use of a cost function taking into account both spatial and statistical properties. The aim is two fold: overcome the trade-off between speckle suppression and details suppression; find a suitable cost function for despeckling in unsupervised learning. The algorithm is validated on both real and simulated data, showing interesting performances.