Adaptive Wavelet-Positional Encoding for High-Frequency Information Learning in Implicit Neural Representation

Implicit Neural Representation (INR) has shown great potential in constructing the complex nature signal as a continuous implicit function. However, the representation results are incomplete since different components of the signal correspond to different frequencies and neural network inherently tends to low-frequency convergence. In this paper, we propose the adaptive Wavelet-Positional Encoding (WPE) to precisely represent content under different frequency distributions for coordinate-based implicit representations. The High-Frequency Perception (HFP) method is first proposed to query locations of high-frequency components from input signals, which can be indicated as local centers of WPE. Then, motivated by wavelet series regression, we present to embed these queried low-dimensional coordinate inputs into wavelet-frequency space by WPE to represent fine details of target signals. Experiments demonstrate that the proposed method can be integrated into various INR methods without modifying training frameworks while significantly improving their performance in 1D signal fitting, 2D image regression, and even 3D scene representation.