PREF: Phasorial Embedding Fields for Compact Neural Representations

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.