Analysis of Downsampling of DCT-Graphs

摘要

The discrete cosine transform (DCT) finds variety of applications in the field of signal processing. Due to its significant data compression properties, it forms a key component of image compression algorithms. Algebraic Signal Processing theory provides a graph representation for the DCT. In this representation, the DCT becomes a special case of Graph Fourier Transform. In this paper, we analyze the DCT in the context of downsampling using various graph-downsampling techniques. We provide proofs for various downsampling outcomes and validate our findings with experiments on 1-D and 2-D data.