Least-Squares Reverse Time Migration With Regularization by Denoising Scheme

Model-based reconstruction offers an effective framework for solving diverse inverse problems in geophysical imaging, and least-squares reverse time migration (LSRTM) can be regarded as a model-based reconstruction method. While LSRTM can produce higher resolution compared to reverse time migration (RTM), it remains prone to challenges such as noise interference, computational complexity, and problems, e.g., artifacts and incomplete illumination. This study adopts the regularization by denoising (RED) strategy to alleviate these issues and further improve imaging resolution and inversion efficiency. The RED technique is notably flexible and requires just a single denoising engine. In our case, it is a filter constructed based on the curvelet transform (CT), which decomposes the imaging into wavelet coefficients of different scales and directions and applies threshold processing to achieve noise suppression. Subsequently, the CT denoising engine is integrated into the explicit RED term, which is formed by the inner product of the imaging result and its denoising residuals. The inversion result is obtained by solving the objective function using the alternating directions method of multipliers (ADMM). The effectiveness of RED-LSRTM is initially tested with the simple flat model, followed by an assessment of its imaging performance on large-angle reflection layers with a layered model. Finally, the RED-LSRTM is assessed in complex geological structures using a salt model.