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Geological sequestration is widely regarded as an effective strategy for mitigating atmospheric CO₂ emissions, yet its success depends on a robust understanding of subsurface fluid transport. Central to this challenge is the ability to characterize permeability heterogeneity at the core scale. Conventional permeability measurements on core plugs provide only bulk-averaged values and are limited in spatial representativeness, while medical CT combined with core-flooding experiments can image core-scale permeability patterns but lacks sufficient resolution. Conversely, micro-CT enables pore-scale characterization and permeability simulation, but its restricted field of view limits assessment of larger-scale heterogeneity. To bridge these scale gaps, this study integrates multi-resolution X-ray CT imaging to capture both pore-scale features and core-scale variability, thereby improving permeability characterization. Four sandstone core-plug samples were scanned at resolutions of 5.0 μm, 22.3 μm, and 68.9 μm. Binary segmentation and pore network models were constructed at each resolution to quantify porosity, pore and throat size distributions, connectivity, and simulated permeability, which were evaluated against laboratory measurements. Simulated permeability derived from 5.0 μm images agrees well with experimental results, whereas simulations based on coarser resolutions are strongly influenced by partial-volume and point-spread effects. Despite this limitation, throat size exhibits robust correlations with experimental permeability across all resolutions. Building on this observation, we introduce the lower partial standard deviation (LPSD), a grayscale-based statistical index that reduces segmentation uncertainty while capturing pore-scale variability. LPSD shows strong positive correlations with pore size, throat size, and experimental permeability at all resolutions. Cross-resolution validation using a heterogeneous sample further demonstrates consistent permeability distributions estimated from LPSD at 22.3 μm and 68.9 μm. Because 68.9 μm resolution is applicable to whole-core CT scanning with Geotek RXCT, the proposed approach enables core-scale permeability mapping that preserves sub-core heterogeneity, providing a more reliable foundation for CO₂ transport modeling, injection strategy design, and long-term storage performance assessment.