Dependence Research on Multi-Layer Convolutions of Images

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.

Automated summary

This paper analyzes the dependence among multi-layer convolutions by examining the gray levels of image pixels before, in, and after the convolutions. The pixels are transformed into modified multifractional Gaussian noise (mmfGn), and their Hurst parameters are calculated. The results show the presence of short-range dependence (SRD) or long-range dependence (LRD), providing valuable insights for designing better network structures and image processing algorithms.