I've just come across a paper that interrelates the covariance matrix of time discrete signals to their autocorrelation function (or a time-delay, respectively), i.e. $$\mathbf{C} = E\{\mathbf{x}\left(t\right)\mathbf{x}^H\left(t-\tau\right)\}.$$
Coming from the image processing field, I have usually just worked for the $\tau = 0$ case, whereas $t$ was just the pixel index instead of a time stamp.
Now, I am wondering how I can transfer the concept of this time delay $\tau$ to image processing.
Side-note: Since I don't use box-car based image processing and determine the pixels for this covariance matrix estimation adaptively, what I have basically is a $\left(K\times N\right)$ data matrix containing $N$ pixels with $K$ "measurements" each.
How can I calculate the time-delayed covariance matrix described in the formula above in my case?