Analysis and Synthesis of 1/f Processes in Images by Graph Fouier Transform

Signals with spectral power density following a specific power law are referred to as 1/f processes. A key characteristic of these processes is that their modeling, estimation, and control can be performed using a single slope parameter. In this study, the adaptation of 1/f processes to two-dimensional (2D) image signals is explored, focusing on image analysis and synthesis based on spectral slope estimation. Image signals are transformed into a one-dimensional frequency spectrum using the Graph Fourier Transform (GFT), enabling the estimation of spectral slopes. GFT is also employed to generate colored noise images with varying slopes. The proposed method has been validated by comparing its accuracy in both analysis and synthesis with Fourier-based approaches, demonstrating the consistency of the results.