Seismic Data Reconstruction Based on Back-Projection Fidelity and Regularization by Denoising Convolutional Neural Network

In this article, we develop a novel reconstruction method that uses sophisticated denoising priors to recover the missing seismic data. First, we construct a regularization item defined by a denoising convolutional neural network (DCNN) and combine it with back-projection fidelity to formulate a novel model for reconstructing missing seismic data. This model incorporates the advantages of regularization by DCNN and back-projection fidelity, which can employ the deep denoising priors learned by the integrated DCNN to obtain excellent reconstruction results with less iterative optimization. Next, we design and deduce an efficient iterative algorithm to minimize the formulated reconstruction model. Concretely, we separate the fidelity and regularization items in the formulated model by employing a generalized approximate message passing strategy, forming a bipartite graph consisting of output and input nodes. Following the first-order necessary condition, we then derive the closed-form solution of each message variable subordinated to the output and input nodes in the bipartite graph, thus resulting in an iterative procedure with multimessage nested passing. Finally, we conduct tests on the feasibility and effectiveness of the proposed algorithm using three datasets. All results prove that the developed method has faster reconstruction efficiency while obtaining higher reconstruction quality in comparison with the conventional sparsity-promoting reconstruction methods.