Light-field (LF) cameras record 4D information about the intensity and angle of light, but limited by the resolution of the sensor, LF images require a trade-off between spatial and angular resolution, which results in generally low spatial resolution for LF images. We work on spatial super-resolution reconstruction (SR) of LF images, but due to the high dimensionality of 4D LF, it is difficult to process it directly, so we decompose 4D LF into low-dimensional sub-spaces. Since the 4D features of interest to different low-dimensional sub-spaces are different, we design a hybrid network structure—HSAESR, which processes multiple low-dimensional sub-spaces individually to adequately model the texture information in the 4D LF. HSAESR is designed to reconstruct Macro Pixel Images (MacPI) and Extremely Planar Images (EPI) respectively, and the final reconstruction results are weighted and fused. For MacPI, a CNN-based feature interaction module is designed using a novel asymptotic ’grid’ interaction approach to fully utilize the correlation between the 2D spatial dimension and the 2D angular dimension sub-spaces in 4D LF. For EPI, a Transformer-based epipolar feature linear complementation module is designed learning global and non-global multi-directional epipolar feature correlations, which learns feature linear correlation factor (α) and linear bias weight (β) through the correlation of non-global epipolar features, and corrects and complements the global epipolar correlation features through feature linear complementation. Extensive experiments are conducted on five datasets, the results show that HSAESR further improves the performance of LF images spatial SR, the reconstruction results are better than the comparison methods.