HOIN: High-Order Implicit Neural Representations
This addresses a key bottleneck in INR for inverse problems, offering a general paradigm that could impact various domains, though it appears incremental as it refines existing cascade structures.
The paper tackles the problem of spectral bias in implicit neural representations (INR) for inverse problems, resulting in overly smooth solutions, and proposes HOIN, a framework that achieves 1 to 3 dB improvements in recovery quality and training efficiency, establishing a new state-of-the-art.
Implicit neural representations (INR) suffer from worsening spectral bias, which results in overly smooth solutions to the inverse problem. To deal with this problem, we propose a universal framework for processing inverse problems called \textbf{High-Order Implicit Neural Representations (HOIN)}. By refining the traditional cascade structure to foster high-order interactions among features, HOIN enhances the model's expressive power and mitigates spectral bias through its neural tangent kernel's (NTK) strong diagonal properties, accelerating and optimizing inverse problem resolution. By analyzing the model's expression space, high-order derivatives, and the NTK matrix, we theoretically validate the feasibility of HOIN. HOIN realizes 1 to 3 dB improvements in most inverse problems, establishing a new state-of-the-art recovery quality and training efficiency, thus providing a new general paradigm for INR and paving the way for it to solve the inverse problem.