Dependence Research on Multi-Layer Convolutions of Images

Abstract

Read online

Convolutions are important structures in deep learning. However, theoretical analysis on the dependence among multi-layer convolutions cannot be found until now. In this paper, the image pixels before, in, and after multi-layer convolutions are of modified multifractional Gaussian noise (mmfGn). Thus, their Hurst parameters are calculated. Based on these, we applied mmfGn model to analyze the dependence of gray levels of multi-layer convolutions of the image pixels and demonstrate their short-range dependence (SRD) or long-range dependence (LRD), which can help researchers to design better network structures and image processing algorithm.

Keywords

• fraction Brownian motion
• Hurst parameter
• time-varying Hurst parameter
• long-range dependence (LRD)
• modified multifractional Gaussian noise
• fractional Gaussian noise (fGn)