wavelet - Shift invariant in wavelet

Question

I always hear that wavelet transform is not shift invariant, and that there are other types of wavelet, like stationary wavelet and double density dual-tree wavelet transform, that are shift invariant.

Can anyone explain to me, what is the meaning of "shift invariant" .

Answer 1

Shift Invariant（时域中的时间不变量）是指给定一个输入及其对应的输出，相同的输入移位后的输出将产生移位的输出。

即，如果 F 是算子，则 OutputImage(x, y) = F(InputImage(x, y))。如果 F 是 Shift Invariant，则表示 OutputImage(x - s1, y - s2) = F(InputImage(x - s1, y - s2))。

在小波世界中，移位不变性的属性通常是通过跳过抽取步骤来实现的。