Efficient Quantization and Denoising Using Local Graph Fourier Frames

Abstract

In our recent work we have proposed a new class of graph signal expansions termed local graph Fourier frames (LGFFs). LGFFs have finite support in the vertex domain and hence entail computationally highly efficient signal analysis and synthesis algorithms. Furthermore, they are extremely flexible and can adapt to a multitude of graph signal types. In this paper, we formulate proof-of-concept approaches for the quantization and denoising of nonstationary graph processes based on LGFFs. We furthermore propose an adaptation of the best basis algorithm to optimally choose the LGFF parameters. Our methods involve simple scalar processing in the LGFF domain and are shown to outperform existing approaches despite having a substantially lower complexity.