提出了一种能够使双随机相位图像加密方法的密文图像保持为非负整数值的变换——重构变换.重构变换包括预处理和频谱搬移两个过程，其主要特点为，在图像进行频域变换之前，通过叠加的方式将整数图像压缩成一半大小的复数图像，从而能缩小后续运算的计算空间；基于重构变换的双随机相位图像加密方法可以实现联合图像压缩和加密的效果.与基于混沌系统的数字图像加密方法相比，本文方法的密文图像具有更低的信息熵.实验结果表明，该方法具有较强的安全性，解密图像基本无失真，并且密文图像对加性噪音攻击具有一定的鲁棒性.

A novel image transforming method called Reconstruction Transform is proposed, which can make the double random phase encryption image become non-negative integer value. Reconstruction transform includes two stages, pre-processing and spectral shifting. It′s major characteristic is that, compress the interger image to become complex image of half-sized before applying spectral transform to the original image, thus reducing the calculation space in the following steps. The proposed method has the advantage of joint image compression and encryption. Compared with the chaotic image encryption scheme, the cipher-text image of the proposed scheme has lower information entropy. Experimental results show that this method has high security, the decrypted image of this method has little distortion and the cipher-text image has a certain degree of robustness to additive noise attack.