为了更有效地滤除数字图像中的噪声，受量子信息处理理论启发，将传统的形态学运算结构元素扩展到叠加态结构元素以更有利于图像的去噪。由于叠加态结构元素只有尺度范围，没有固定的大小和形状，因此可表示为该尺度范围内的各种不同大小和形状的传统结构元素的线性叠加，并在受到测量时可坍缩到其中的某一传统结构元素。该文首先定义了一个基于叠加态结构元素的坍缩形态学算子，然后在此基础上构建了一种基于均方差的自适应形态滤波方法。计算机仿真实验表明，该滤波方法与中值滤波和传统的形态滤波方法相比较，有更强的噪声滤除能力，并且对噪声的强度不敏感。

The structure element (SE) used in morphology operation is extended to superposition of SE, short for SSE, inspired by the quantum information processing theory.The SSE’s has no fixed sizes or form and its scale is described with the limits of size. SSE is linear superposition of all SE available in its limits of size. SSE can be collapsing and returns to a SE when a measurement on it is taken. The morphological operators, named by collapsing morphological operators, based on quantum measurement and collapsing are defined,and then a self-adapted filtering operation is created by applying these operators in this paper. The results obtained in the computer simulation on image filtering using this operation is shown that this self-adapted filtering has more powerful ability for denoising than median filter and corresponding traditional morphological filter and are independent of the intensity of noise.