Implicit Neural Representation (INR) as a mighty representation paradigm has achieved success in various computer vision tasks recently. Due to the low-frequency bias issue of vanilla multi-layer perceptron (MLP), existing methods have investigated advanced techniques, such as positional encoding and periodic activation function, to improve the accuracy of INR. In this paper, we connect the network training bias with the reparameterization technique and theoretically prove that weight reparameterization could provide us a chance to alleviate the spectral bias of MLP. Based on our theoretical analysis, we propose a Fourier reparameterization method which learns coefficient matrix of fixed Fourier bases to compose the weights of MLP. We evaluate the proposed Fourier reparameterization method on different INR tasks with various MLP architectures, including vanilla MLP, MLP with positional encoding and MLP with advanced activation function, etc. The superiority approximation results on different MLP architectures clearly validate the advantage of our proposed method. Armed with our Fourier reparameterization method, better INR with more textures and less artifacts can be learned from the training data.

翻译：隐式神经表示作为一种强大的表示范式，近年来在各类计算机视觉任务中取得了显著成功。针对传统多层感知机存在的低频偏好问题，现有研究已探索了位置编码、周期激活函数等先进技术以提高INR的准确性。本文创新性地将网络训练偏差与重参数化技术相结合，从理论上证明了权重重参数化可有效缓解MLP的谱偏差。基于理论分析，我们提出了一种傅里叶重参数化方法，该方法通过学习固定傅里叶基的系数矩阵来重构MLP权重。我们在不同MLP架构（包括标准MLP、带位置编码的MLP及采用先进激活函数的MLP等）的INR任务上评估了所提傅里叶重参数化方法。不同MLP架构上的优异逼近结果清晰验证了我们方法的优势。结合傅里叶重参数化方法，可从训练数据中学习到纹理更丰富、伪影更少的优质隐式神经表示。