A comparative study over improved fast iterative shrinkage-thresholding algorithms: an application to seismic data reconstruction

Seismic data reconstruction is a crucial process involving the restoration of missing or corrupted traces to create a uniform dataset for subsequent data processing. Various factors such as equipment failures, and surface obstacles, result in irregularly located or corrupted traces. The absence of these traces can compromise the quality and accuracy of the resulting image. To address this issue, the Nonuniform Fast Fourier Transform (NUFFT) method is employed to reconstruct missing traces in datasets with non-uniformly sampled data. It works by interpolating the non-uniformly sampled data onto a regular grid, enabling the traditional Fast Fourier Transform application for data recovery. This interpolation process is adjusted using a kernel function to account for non-uniform sampling and reduce aliasing artifacts. The outcome is a collection of Fourier coefficients that can be utilized to reconstruct missing or incomplete parts of data. This problem is transformed into a linear constraint problem, which is efficiently solved using the Fast Iterative Shrinkage-Thresholding Algorithm (FISTA). In this study, we explore various techniques aimed at improving the convergence of FISTA, collectively referred to as improved FISTA methods. To validate the NUFFT+FISTA method for data reconstruction, we conducted numerical tests using 3D and 2D synthetic datasets, as well as field data. These tests show the advantages of the Greedy-FISTA in terms of convergence rate and affirm the accuracy of this approach in filling missing data traces.