Curvelet Based Multiresolution Analysis of Graph Neural Networks

Multiresolution techniques are deeply related to image/signal processing, biological and computer vision, scientific computing, optical data analysis. Improving quality of noisy signals/images has been an active area of research in many years. Although wavelets have been widely used in signal processing, they have limitations with orientation selectivity and hence, they fail to represent changing geometric features along edges effectively. Curvelet transform on the contrary exhibits good reconstruction of the edge data by incorporating a directional component to the conventional wavelet transform and can be robustly used in the analysis of complex neural networks; which in turn are represented by graphs, called Graph Neural Networks. This paper explores the application of curvelet transform in the analysis of such complex networks. Especially, a technique of Fast Discrete Curvelet Transform de-noising with the Independent Component Analysis (ICA) for the separation of noisy signals is discussed. Two different approaches viz. separating noisy mixed signals using fast ICA algorithm and then applying Curvelet thresholding to de-noise the resulting signal, and the other one that uses Curvelet thresholding to de-noise the mixed signals and then the fast ICA algorithm to separate the de-noised signals are presented for the purpose. The Signal-to-Noise Ratio and Root Mean Square Error are used as metrics to evaluate the quality of the separated signals.