Data-driven Optimization of Row-Column Transforms for Block-Based Hybrid Video Compression

In state-of-the-art video compression residual coding is done by transforming the prediction error signals into a less correlated representation and performing the quantization and entropy coding in the transform domain. For complexity reasons usually separable transforms are used. A more flexible transform structure is given by row-column transforms, which apply a separate transform to each row and each column of a signal block. This paper describes a method for training such structured transforms by maximizing the data likelihood under a parameterized probabilistic model with a compelled structure. An explicit model is derived for the case of row-column transforms and its efficiency is demonstrated in the application of video compression. It is shown that trained row-column transforms achieve almost the same coding gain as unconstrained KLTs when applied as secondary transforms, while the encoder and decoder runtime are the same as in the separable transform case.