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中文摘要：
目的图像的表达始终是图像处理领域的基础问题之一，本文研究了数字图像表达为一个复数的方法，进一步将这种表示方法应用于图像伪装。方法在位值制记数法中，取复数为基，将数字图像在复数基下表达为一个高斯整数，从而将图像与复平面上的点建立对应关系。这种数字图像表达方法，能够将图像间的关系转化为复平面上点之间的关系，从而借助几何学方法研究图像问题。据此实现了一种图像伪装算法。结果该算法不仅可以伪装一幅图像，还可以同时伪装多幅图像，也可以进行一幅图像的多次伪装。结论实验检测结果表明该伪装算法数值稳定，在理想传输环境下可准确恢复图像，如果传输过程中受到噪声污染，也能较好地恢复保密图像。
英文摘要：
Objective Image representation has always been a basic problem in image processing. This paper studies the ap- proach of a digital image expressed as a complex number. The new approach has been applied to image disguise, and the result is satisfying. Method A one-to-one correspondence established between an image and a point in a complex plane based on complex bases under positional number system notation. The relationships between different images can be conver- ted into a plain vector operation, which helps image study using geometric method. Thus, a new image disguise method is realized. Result This image disguise algorithm can not only disguise one or many images, but also allows an image to be disguised many times. Conclusion Experimental results show that our method is numerically stable, can accurately restore secret images in an ideal transmission environment, and can restore secret images with some satisfaction even in a noisy transmission environment.
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