Texture analysis in T1-Weighted Magnetic Resonance Imaging (T1WI) with high spatial resolution can identify unique texture patterns in brain tissue associated with Alzheimer's Disease (AD). However, texture feature extraction from Low-Resolution (LR) T1WI presents significant technical challenges due to inherent information loss. In this work, we proposed TE-CGAN, a Texture-Enhanced Cycle Generative Adversarial Network for high-quality texture feature extraction from LR T1WI. Specifically, a hybrid loss was constructed to transform the complex voxel-wise multi-feature encoding learning task into multiple low-dimensional learning tasks, including structural preservation, perceptual consistency, and texture enhancement, to increase the global and local quality of synthesized T1WI. A total of 1358 scans of brain T1WI from 995 subjects derived from data pools of neural imaging research in Tongji Hospital (781 subjects, 1144 scans) and Xuanwu Hospital (214 subjects, 214 scans) were included. In parallel comparison with six generated methods, we comprehensively evaluated (a) the quality of synthesized imaging, (b) the precision of texture features, and (c) AD-related application scenarios. Compared with other methods included in our study, TE-CGAN-synthesized T1WI demonstrated superior performance across both conventional image quality metrics (Peak Signal-to-Noise Ratio = 30.23 dB; Structural Similarity Index = 0.88) and texture feature fidelity (Pearson Correlation = 0.93). Even without retraining or fine-tuning, TE-CGAN demonstrated superior performance in texture-based clinical diagnosis within the external test set compared to other approaches. Our study validated the use of TE-CGAN for enhancing LR T1WI texture features, demonstrating potential application value in clinical practice and neuroscience research.