DCT and DST Filtering With Sparse Graph Operators

Graph filtering is a fundamental tool in graph signal processing. Polynomial filters (PGFs), defined as polynomials of operator, can be implemented the vertex domain, and usually have lower complexity than frequency domain filter implementations. In this paper, we focus on design for graphs with Fourier transform (GFT) corresponding to discrete trigonometric (DTT), i.e., one 8 types cosine transforms (DCT) sine (DST). case, show that multiple sparse operators identified, which allows us propose generalization PGF design: multivariate polynomial (MPGF). First, widely used DCT-II (type-2 DCT), characterize set share matrix their common eigenvector matrix. This contains well-known connected line graph. These viewed operating DCT approximate any by MPGF, leading more degrees freedom conventional approach. Then, extend those results all 16 DTTs well 2D versions, how associated sets determined. We demonstrate experimentally ideal low-pass exponential DCT/DST approximated higher accuracy similar runtime complexity. Finally, apply our method transform-type selection video codec, AV1, where significant encoding time savings, negligible compression loss.