GNGTS 2018 - 37° Convegno Nazionale

756 GNGTS 2018 S essione 3.3 In our problem, the model weights w are estimated by minimizing the mean squared error between P k and Pˆ k , over all patches in the training set. As in standard CNN training, we follow an iterative procedure to minimize the loss function, stopping at the iteration where the error over the validation set is minimum. Specifically, we use Adam optimization algorithm with learning rate and patience initialized at 0.01 and 10, respectively. The former is decimated while the latter is halved in presence of plateau of the cost function. We verified that the smallest validation loss is achieved within only 30 training epochs. System Deployment. When a new corrupted image Ī which has never been seen by the U-net is under analysis, its inpainted version is estimated as follows: a set of K patches is obtained from the image as described above. Each patch P - k is processed by the architecture in order to estimate the reconstructed patch Pˆ k . Finally, to reconstruct the image Iˆ , all the estimated patches Pˆ k are re-assembled together by sample-wise averaging the overlapping portions. Results. We exploited the Mobil Avo Viking Graben Line 12 dataset (Keys, 1998), from now on V for brevity, which consists of N = 1001 gray-scale seismic images. Specifically, each image I ∈ ℝ 1024 × 128 : rows represent time domain, sampled every 4 ms; columns are in spatial domain with 25 m of sampling. In order to simulate the lack of seismic acquisitions, we delete a percentage H of the available data traces. To be precise, for each acquired image I , we randomly delete the H% of its traces, H ∈ {10, 30, 50}, obtaining a holed image Ī . Thus, we generate 3 different datasets V H : V 10 , V 30 , V 50 , each one including N seismic images with increasing amount of missing traces. For the sake of clarity, Fig. 3(a) reports an example of original image I and related Ī according to different percentages H . Fig. 3 - (a) From left to right: original dense image I, image Ī ∈ V 10 , image Ī ∈ V 30 , image Ī ∈ V 50 . (b) From left to right: original dense image I, image Î ∈ V 10 , image Î ∈ V 30 , image Î ∈ V 50 .