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Screen photos often suffer from moiré patterns, which significantly affect their visual quality. Although many deep learning-based methods for removing moiré patterns have been proposed, they fail to recover images with complex textures and heavy moiré patterns. Here, we focus on text images with heavy moiré patterns and propose a new demoiré approach, incorporating frequency-domain peak filtering and spatial-domain visual quality enhancement. We find that the content of the text image mainly lies in the central region, whereas the moiré pattern lies in the peak region, in the frequency domain. Based on this observation, a peak-filtering algorithm and a central region recovery strategy are proposed to accurately locate and remove moiré patterns while preserving the text parts. In addition, to further remove the noisy background and paint the missing text parts, an image enhancement algorithm utilising the Otsu method is developed. Extensive experimental results show that the proposed method significantly removes severe moiré patterns from images with better visual quality and lower time cost compared to the state-of-the-art methods. [ABSTRACT FROM AUTHOR]