# How to understand the de-correlation property of DCT? What does de-correlation mean?

Here are three problems that I can't understand:

1. Usually what does de-correlation mean in image-processing?

2. What's the benefit of de-correlation when it comes to image splicing?

3. Is there some relationship among neighbouring coefficients? And I read a paper which says coefficients difference matrix(got by coefficients subtracting its neighbor) can eliminate the relationship of the coefficients，How to understand this?

I would really appreciate if someone can help me!

3. Generally yes, unless you have uncorrelated noise in your images. A classical and simple model is an order-one Markov or autoregressive process. Basically a pixel somehow depends (with a parameter $$\rho$$) on the past pixel, with uncertainty. If $$\rho$$ is close to $$0$$, you are already decorrelated. If $$\rho$$ is close to $$1$$ (typically $$0.90-0.95$$), the data is quite correlated.