Image fine-grained enhancement faces the challenge of accurately extracting detailed edge information, which is crucial for improving image quality and emphasizing critical visual structures. To address this issue, this paper focuses on developing an effective fine-grained edge enhancement approach that integrates precise edge extraction into the image enhancement process. Traditional edge extraction methods are predominantly gradient-based, detecting significant pixel intensity changes but often failing to capture subtle structural details. Given these limitations, phase-based methods such as the Riesz transform provide multi-scale and multi-directional information, making them more suitable for fine-grained edge detection and enhancement. This paper proposes a fine-grained edge enhancement network architecture based on the Riesz transform, specifically designed to effectively capture edge features and enhance classification accuracy. In this approach, the fine-grained edge information generated using the Riesz transform is incorporated into the proposed multi-channel CNN (Convolutional Neural Network) model through additional channels, participating in the training process alongside the original image information. This multi-channel architecture allows the model to effectively utilize both original and enhanced fine-grained edge features, thereby improving its overall performance in fine-grained image analysis. Experiments on five widely used datasets indicate that the proposed method achieves consistent improvements over baseline CNNs. An ablation study further shows that treating Riesz features as an additional input dimension is more effective than direct superposition. Overall, the method not only enhances classification accuracy across diverse datasets but also demonstrates good robustness and generalization ability.