Half-Quadratic Splitting with Learned Regularization for Image-Domain Least-Squares Migration of Marine Seismic Data

Marine seismic imaging is affected by limited acquisition aperture, nonuniform illumination, and complex features such as seafloor structures and low-velocity gas clouds. These factors can produce blurred reflectors, amplitude imbalance, and migration artifacts in conventional reverse-time migration (RTM). Point-spread-function (PSF)-based image-domain least-squares migration (ID-LSM) compensates for spatially varying imaging responses through deconvolution, but its ill-conditioned inverse problem can amplify weakly constrained spectral components. We propose HQS-LR, an HQS-inspired, physics-guided unrolled framework for PSF-based ID-LSM. Each of its T stages performs a closed-form Fourier-domain PSF-based data-consistency update, applies a U-Net-based module for learned structural regularization and reflectivity refinement, and fuses the two estimates using a relaxation weight. HQS-LR is trained end-to-end using supervised triplets of reflectivity patches, migrated-image patches, and PSF patches generated from the Marmousi model. Sequential calibration on the Sigsbee2A synthetic model selects a six-stage configuration for the subsequent experiments. In the Sigsbee2A calibration-set comparison, this configuration achieves a Pearson correlation coefficient (CC) of 0.681 and a normalized PSF forward-matching residual of 0.035, providing a favorable balance between reflectivity similarity and consistency with the PSF imaging model while reducing ringing and preserving reflector continuity and fault geometry. Applied to the Mobil AVO Viking Graben Line 12 dataset, HQS-LR improves reflector focusing and continuity, suppresses localized oscillatory artifacts, and exhibits broader effective wavenumber support than the evaluated alternatives. These results indicate the potential of combining PSF-based physical constraints with learned structural priors for marine seismic reflectivity inversion.