DCTs, DSTs and transforms on path graphs: History and recent results

Soon after turning 50, the DCT remains the dominant transform for image and video coding and by far the most popular among the family of discrete trigonometric transforms (DTTs), including the DCTs and DSTs. The connection between the DCT and eigendecompositions of path graphs has been known for at least 30 years, yet DTT extensions that leverage this graph interpretation have only emerged recently. In this talk, we provide an overview of the DCT and its connection to graphs and describe several recent graph-based extensions of the DCT having desirable properties. Among these extensions, we will describe graph-based transforms that are efficiently learnable from data, have computationally efficient implementations, or are optimized for perceptual and/or computational metrics (rather than mean squared error distortion).