Fractals in graph signal

Abstract

The focus of this project is to analyze and study the amalgamation of two very promising fields graph signal processing and fractality analysis, inspired by an extensive review of existing litera- ture on fractal dimensions, signal categorization, and wavelet transforms. This project explores the effectiveness of these methods in classifying and analyzing signals on irregular graphs, often found in real-world networks. Initial study and experiments involve calculating fractal dimen- sions to understand signal complexity and applying wavelet transforms for decomposition. In the duration of this study we explore various methods for fractal dimension estimation and how it be applied on graph signals. The initial phase of this project is focused on exploring existing literature and implementing the same in the context of graph signals. We also explore multifractal analysis for graph signals to enhance tasks like denoising and anomaly detection. Preliminary results are promising, suggesting that integrating fractal and wavelet methodologies into GSP could significantly advance the field of signal processing.