Unsupervised FISTA-Net-Based Adaptive Subtraction for Seismic Multiple Removal

Adaptive subtraction plays a crucial role in the multiple removal method that involves modeling and subtraction steps. The linear regression (LR)-based method utilizes the fast iterative shrinkage thresholding algorithm (FISTA) to solve the optimization problem that contains the
${L}1$
norm minimization constraint of primaries. It selects the regularization factor and shrinkage thresholding value through trial and error. Under the non-LR framework, the U-net is used for adaptive subtraction of modeled multiples from the original recorded data. Since U-net has a large network capacity, it is prone to overfit to the original recorded data and lead to primary damage. In this article, we unfold the iterative steps of FISTA to construct FISTA-Net, which takes the original recorded data and modeled multiples as input data and outputs the estimated primaries. The FISTA-Net-based method does not require true primaries as labels and uses the
${L}1$
norm minimization constraint of primaries for unsupervised training. It can adaptively estimate the regularization factor and shrinkage thresholding value, which is replaced by U-net. FISTA-Net introduces the nonlinear mapping ability of U-net into its structure, which can be interpreted as the iterative steps of FISTA. As a result, the proposed FISTA-Net-based method can better attenuate residual multiples, avoid overfitting, and preserve primaries compared to the LR-based and U-net -based methods.