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The development of high-resolution two-dimensional spectral estimation techniques is of notable interest in synthetic aperture radar (SAR) imaging. Typically, data-independent techniques are exploited to form the SAR images, although such approaches will suffer from limited resolution and high sidelobe levels. Recent work on data-adaptive approaches have shown that both the iterative adaptive approach (IAA) and the sparse learning via iterative minimization (SLIM) algorithm offer excellent performance with high-resolution and low side lobe levels for both complete and incomplete data sets. Regrettably, both algorithms are computationally intensive if applied directly to the phase history data to form the SAR images. To help alleviate this, efficient implementations have also been proposed. In this paper, we further this work, proposing yet further improved implementation strategies, including approaches using the segmented IAA approach and the approximative quasi-Newton technique. Furthermore, we introduce a combined IAA-MAP algorithm as well as a hybrid IAA- and SLIM-based estimation scheme for SAR imaging. The effectiveness of the SAR imaging algorithms and the computational complexities of their fast implementations are demonstrated using the simulated Slicy data set and the experimentally measured GOTCHA data set.