Factorization of the coefficient variance matrix in orthogonal transforms

The authors derive a matrix factorization of the coefficient variances for any fixed transformation. This factorization formulation provides a better framework for understanding the role of transform on the one hand, and the signal source model on the other. It also greatly simplifies the number of computational operations required for each variance calculation. A transform-specific matrix which links the transform to the signal correlation model is derived. This factorization provides a conceptual framework for understanding the behaviour of the transform for different source models. It also significantly simplifies the calculation of the variance of each transform coefficient from a quadruple sum over four indices to a double sum over two indices. This simplification can be used in adaptive transform coding which requires an estimate of the variances. Test results demonstrate that this mode-based variance calculation provides an accurate basis for adaptive transform coding, particularly at low bit rates