Cross-Frequency Implicit Neural Representation with Self-Evolving Parameters.

Area of Science:

• Computer Vision
• Machine Learning
• Signal Processing

Background:

• Implicit Neural Representations (INRs) are effective for visual data but struggle with mixed frequencies and manual parameter tuning.
• Classical INRs require manual configuration of parameters like frequency ($\omega$) and rank (R), limiting their adaptability.
• Representing data in its original space mixes frequency components, hindering precise characterization.

Purpose of the Study:

• To propose a novel self-evolving cross-frequency INR (CF-INR) that decouples data into distinct frequency components.
• To enhance data representation accuracy by employing INRs in the wavelet space for separate frequency characterization.
• To introduce a self-evolving parameter optimization for INRs, eliminating manual tuning and enabling dataset-specific configurations.

Main Methods:

• Utilized Haar wavelet transform to decompose visual data into four frequency components.
• Employed INRs within the wavelet space for distinct characterization of each frequency component.
• Developed a cross-frequency tensor decomposition paradigm with self-evolving parameters (R and $\omega$) for automated optimization.

Main Results:

• CF-INR achieved higher accuracy in visual data representation by handling frequency components separately.
• The self-evolving optimization automatically adjusted rank (R) and frequency ($\omega$) parameters for each component.
• Demonstrated superior performance of CF-INR over state-of-the-art methods in image regression, inpainting, denoising, and cloud removal tasks.

Conclusions:

• CF-INR offers a more accurate and automated approach to visual data representation compared to classical INRs.
• The self-evolving cross-frequency paradigm effectively addresses the limitations of manual parameter tuning in INRs.
• CF-INR shows significant potential for various inverse imaging problems and visual data processing applications.