Compact Neural Field Representation via Multi-scale Tensor Decomposition

We propose a novel approach that leverages the principles of tensor decomposition to improve parameter efficiency in neural field representation. Previous grid-based methods typically densely distribute learnable features across grid points to represent underlying images or 3D shapes. While achieving promising results, most grids are redundant due to not fully leveraging the low-rank properties of underlying signals. To tackle this issue, we introduce multi-scale tensor decomposition to transform the high-dimensional spatial signal into a composition of multiple low-dimensional vectors. We observe that signals may contain varying levels of information at different scales, prompting us to adjust the rank of tensor decomposition accordingly for each scale. Subsequently, the queried feature undergoes further processing with multi-frequency sinusoid functions to distinguish signals at different frequencies. Our representation achieves state-of-the-art results in the final reconstruction quality while notably reducing the number of parameters. We will open-source the code after the paper is accepted.