Efficient quantization and denoising using local graph Fourier frames

Abstract

In our recent work we have proposed a new class of graph signal expansion termed local graph Fourier frames (LGFF). LGFF 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 discuss proof-of-concept approaches for the quantization and denoising of nonstationary graph processes based on LGFF. 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 in spite of having a substantially lower complexity.