Video Coding - Understanding Transforms

• Transformation coding is orthogonal transformation, which can be understood as coordinate axis rotation• The purpose of the transform is: to de-correlate the signal, to make the signal independent, to take the independent quantization of the transform coefficient, to minimize the distortion, and to obtain a lower code rate• Transform + scalar quantization can obtain memory gain in vector quantization• The geometric mean of the variance of the transform coefficients of a good transform is as small as possible, which means that the variance of the transform coefficients is large, and the variance of the transform coefficients is small.• The greater the correlation of the sources, the greater the gain obtained by the transformation• Pareto condition• Common transformations○ KLT Transformation§ Most de-correlated§ Different sources, different transformation matrices§ Optimal transformation under MSE§ Since the transformation coefficients must be recalculated for each different source, it is more complicated, and the transmission of the transformation coefficients requires additional code rate consumption, which is not commonly used.○ DCT Transform§ Different sources, the same transformation matrix§ The source correlation tends to 1, and the performance of DCT and KLT tends to be consistent○ The algorithm complexity of 2-dimensional separable transform is O(N^4) compared to 2-dimensional non-separable transform becomes O(N^3).