We present a phasorial embedding field \emph{PREF} as a compact representation to facilitate neural signal modeling and reconstruction tasks. Pure multi-layer perceptron (MLP) based neural techniques are biased towards low frequency signals and have relied on deep layers or Fourier encoding to avoid losing details. PREF instead employs a compact and physically explainable encoding field based on the phasor formulation of the Fourier embedding space. We conduct a comprehensive theoretical analysis to demonstrate the advantages of PREF over the latest spatial embedding techniques. We then develop a highly efficient frequency learning framework using an approximated inverse Fourier transform scheme for PREF along with a novel Parseval regularizer. Extensive experiments show our compact PREF-based neural signal processing technique is on par with the state-of-the-art in 2D image completion, 3D SDF surface regression, and 5D radiance field reconstruction.
翻译:我们展示了一种速成嵌入字段 \ emph{ PREF}, 作为一种促进神经信号建模和重建任务的缩略语。 基于纯多层天体(MLP) 的神经技术偏向于低频信号,并依靠深层或Freyer编码来避免丢失细节。 PROF 则使用基于Fourier嵌入空间的条子配制的紧凑和可实际解释的编码字段。 我们进行了全面的理论分析,以展示PREF相对于最新的空间嵌入技术的优势。 然后,我们开发了一个高效的频率学习框架,对PREF 使用一种近似为逆向的四极变换方案, 以及一个新型的Prassval正规化器。 广泛的实验显示,我们基于紧凑 PREF 的神经信号处理技术与 2D 图像完成、 3D SDF 表面回归和 5D 弧度场重建相同。