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We propose a super-resolution algorithm that combines spatially variant apodization (SVA) with a modified geometric mean filter to improve the resolution of synthetic aperture radar (SAR) images and reduce sidelobes simultaneously. This method does not require iterative calculation. The efficacy of the proposed algorithm is verified by simulation with point targets and in experiments with a real SAR image. The proposed method improved resolution by 40% compared to SVA and phase-extension inverse filtering.