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The existing deep-learning-based hyperspectral anomaly detection methods detect anomalies by reconstructing a clean background. However, these methods model the background of the hyperspectral image (HSI) through global features, neglecting local features. In complex background scenarios, these methods struggle to obtain accurate background priors for training constraints, thereby limiting the anomaly detection performance. To enhance the capability of the network in extracting local features and improve anomaly detection performance, a hyperspectral anomaly detection method based on differential network is proposed. First, we posit that anomalous pixels are challenging to be reconstructed through the features of surrounding pixels. A differential convolution method is introduced to extract local punctured neighborhood features in the HSI. The differential convolution contains two types of kernels with different receptive fields. These kernels are adopted to obtain the outer window features and inner window features. Second, to improve the feature extraction capability of the network, a local detail attention and a local Transformer attention are proposed. These attention modules enhance the inner window features. Third, the obtained inner window features are subtracted from the outer window features to derive differential features, which encapsulate local punctured neighborhood characteristics. The obtained differential features are employed to reconstruct the background of the HSI. Finally, the anomaly detection results are extracted from the difference between the input HSI and the reconstructed background of the HSI. In the proposed method, for each receptive field kernel, the optimization objective is to reconstruct the input HSI rather than the background HSI. This way circumvents problems where the background constraint biases might affect detection performance. The proposed method offers researchers a new and effective approach for applying deep learning in a local area to the field of hyperspectral anomaly detection. The experiments are conducted with multiple metrics on five real-world datasets. The proposed method outperforms eight state-of-the-art methods in both subjective and objective evaluations. [ABSTRACT FROM AUTHOR]