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.

通过提出一种称为 High-Order Implicit Neural Representations (HOIN) 的通用框架，通过增强模型的表达能力和减轻频谱偏差，加速和优化逆问题的解决，HOIN 在大多数逆问题中实现了 1 到 3 dB 的改进，从而为逆问题的解决提供了一种新的通用范例。