# 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!

## 1 Answer

1. The term "decorrelation" generally accounts for processing that reduce autocorrelation within single, or cross-correlation within a group of signals or images. Doing that, it should preserve important features in the data.

2. In other terms, images often contains simpler "objects" (in terms of morphology: bumps, edges, textures) that are mixed, or distorted. Generally, unmixing them via decorrelation somehow simplify further processing.

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.

The DCT was meant for diagonalizing the resulting autocovariance matrices with Toeplitz structure, to give fast estimates of their eigenvectors. Transforming a fat autocovariance matrix into a thin, close to a diagonal, matrix is an instance of decorrelation.