  We consider the problem of 3D seismic inversion from pre-stack data using a
very small number of seismic sources. The proposed solution is based on a
combination of compressed-sensing and machine learning frameworks, known as
compressed-learning. The solution jointly optimizes a dimensionality reduction
operator and a 3D inversion encoder-decoder implemented by a deep convolutional
neural network (DCNN). Dimensionality reduction is achieved by learning a
sparse binary sensing layer that selects a small subset of the available
sources, then the selected data is fed to a DCNN to complete the regression
task. The end-to-end learning process provides a reduction by an
order-of-magnitude in the number of seismic records used during training, while
preserving the 3D reconstruction quality comparable to that obtained by using
the entire dataset.
