Deep preconditioners and their application to seismic wavefield processing

Seismic data processing heavily relies on the solution of physics-driven inverse problems. In presence unfavourable acquisition conditions (e.g., regular or irregular coarse sampling sources and/or receivers), underlying problem becomes very ill-posed and prior information is required to obtain a satisfactory solution. Sparsity-promoting inversion, coupled with fixed-basis sparsifying transforms, represent go-to approach for many tasks due its simplicity implementation proven successful application in variety scenarios. Nevertheless, such transforms rely assumption that seismic can be represented as linear combination finite number basis functions. Such an may not always fulfilled, thus producing sub-optimal solutions. Leveraging ability deep neural networks find compact representations complex, multi-dimensional vector spaces, we propose train AutoEncoder network learn nonlinear mapping between input representative latent manifold. The trained decoder subsequently used preconditioner at hand. Through synthetic field examples, proposed nonlinear, learned transformations are shown outperform converge faster sought tasks, ranging from deghosting wavefield separation both regularly irregularly subsampled data.