The Fractional Fourier Transform (FRFT) has been playing a unique and increasingly important role in signal and image processing. In this letter, we investigate the property of frequency shift in two-dimensional FRFT (2D-FRFT) domain. It is shown that the magnitude of image reconstruction from phase information is frequency shift-invariant in 2D-FRFT domain, enhancing the robustness of image encryption, an important multimedia security task. Experiments are conducted to demonstrate the effectiveness of this property against the frequency shift attack, improving the robustness of image encryption.

中文翻译：

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2D-FRFT域的频移特性及其在图像加密中的应用

分数阶傅立叶变换（FRFT）在信号和图像处理中一直发挥着独特的作用，并且日益重要。在这封信中，我们研究了二维FRFT（2D-FRFT）域中的频移特性。结果表明，从相位信息重建图像的幅度在2D-FRFT域中是频移不变的，从而增强了图像加密的鲁棒性，这是一项重要的多媒体安全任务。进行实验以证明该特性对频移攻击的有效性，从而提高了图像加密的鲁棒性。