GNGTS 2018 - 37° Convegno Nazionale

GNGTS 2018 S essione 3.1 585 corresponding desired outputs I ( k ) ref and it learns how to produce an output Î ( k ) by minimizing an appropriate cost function. We propose to use a generative adversarial network (GAN), that is logically split in two components: i) the generator that takes care of the input-output image mapping (i.e. Î = G(I) ); ii) a discriminator D that aims at distinguishing between generated images Î and the reference ones I ref . As architectures, we followed the guidelines proposed by Isola (2017). Specifically, the generator is a U-net (fully-convolutional autoencoder with 5 levels and skipped connections, for a total amount of more than 42 million parameters). On the other hand, the discriminator is a shallower fully connected network composed by a series of convolutional, pooling and rectified linear unit layers. The rationale behind GAN training is that the discriminator is a binary classifier aimed at predicting whether the input was original or synthesized by the generator; at the same time, the generator is trained to obtain the desired output from a given input and fool the discriminator. In other words, the discriminator can be seen as a regularizer of the generator, since it enforces the generator to output images visually similar to real ones. The training cost function (usually referred to as loss ) depends on several terms. One term is the generator loss, defined as which is the L1 distance between the desired and the actual output of the generator; this term controls that the generated image is coherent with the desired one. An additional term is the GAN loss: which is a binary cross-entropy and measures how likely the generator is able to fool the discriminator. Finally, we propose to add a normalization term: that enforces the generated image to have a small p-norm as typically required in some seismic imaging applications. The overall loss function to minimize is where λ 1 , λ 2 control the weights of the different loss terms. To adapt the proposed methodology to images of any size, the network is built to work on image patches of N by M samples each, that can be either overlapped or adjacent. Once the patches have been processed, the whole image is reconstructed by a simple overlap-and- average step. Applications. In this section we discuss the investigated applications, providing all the details about the datasets and the achieved results. In our work, minimization is achieved by the Adam optimizer (Kingma 2014). Regarding the patches, we fixed the dimensions to have squared 128x128 patches, with no overlap. Both the examples run on a workstation mounting a Nvidia Titan X, 32GB of RAM and an Intel i7-2600 CPU; indeed, the computational power required is not prohibitive. Concerning the loss function, we choose λ 1 = 100 and λ 2 = 10. High quality images from coarse data. Let us consider a fast track project: we would like to obtain high quality migrated images, but we have no time/resources to perform Reverse