Learning separable transforms by inverse covariance estimation
Orthogonal transforms are one of the most important components of a video encoder system. They are applied to residual block images obtained as the difference between a target and its prediction. In this paper we propose a framework to design separable transforms from prediction residual statistics. We model the data as a 2D Gaussian Markov random field and approximate its inverse covariance by a matrix with a separable structure, thus explicitly constructing a separable orthonormal matrix that approximates the KLT. Our designed transforms can adapt to prediction residual statistics, have low complexity (compared to non separable transforms), require selecting few parameters and outperform hybrid DCT/ADST separable transform for intra coding of AV1 residuals.