We present an efficient frequency-based neural representation termed PREF: a shallow MLP augmented with a phasor volume that covers significant border spectra than previous Fourier feature mapping or Positional Encoding. At the core is our compact 3D phasor volume where frequencies distribute uniformly along a 2D plane and dilate along a 1D axis. To this end, we develop a tailored and efficient Fourier transform that combines both Fast Fourier transform and local interpolation to accelerate naïve Fourier mapping. We also introduce a Parsvel regularizer that stables frequency-based learning. In these ways, Our PREF reduces the costly MLP in the frequency-based representation, thereby significantly closing the efficiency gap between it and other hybrid representations, and improving its interpretability. Comprehensive experiments demonstrate that our PREF is able to capture high-frequency details while remaining compact and robust, including 2D image generalization, 3D signed distance function regression and 5D neural radiance field reconstruction.

翻译：我们提出一种高效的基于频率的神经表示，称为PREF：一个浅层MLP，辅以相量体积，覆盖了比先前傅里叶特征映射或位置编码更显著的边界频谱。其核心是我们紧凑的三维相量体积，其中频率沿二维平面均匀分布并沿一维轴扩张。为此，我们开发了一种定制的、高效的傅里叶变换，结合了快速傅里叶变换和局部插值，以加速朴素傅里叶映射。我们还引入了一个帕塞瓦尔正则化项，以稳定基于频率的学习。通过这些方式，我们的PREF减少了基于频率表示中昂贵的MLP，从而显著缩小了其与其他混合表示之间的效率差距，并提高了其可解释性。综合实验表明，我们的PREF能够捕捉高频细节，同时保持紧凑和鲁棒性，包括二维图像泛化、三维符号距离函数回归和五维神经辐射场重建。