The ability to learn compact, high-quality, and easy-to-optimize
representations for visual data is paramount to many applications such as novel
view synthesis and 3D reconstruction. Recent work has shown substantial success
in using tensor networks to design such compact and high-quality
representations. However, the ability to optimize tensor-based representations,
and in particular, the highly compact tensor train representation, is still
lacking. This has prevented practitioners from deploying the full potential of
tensor networks for visual data. To this end, we propose 'Prolongation
Upsampling Tensor Train (PuTT)', a novel method for learning tensor train
representations in a coarse-to-fine manner. Our method involves the prolonging
or `upsampling' of a learned tensor train representation, creating a sequence
of 'coarse-to-fine' tensor trains that are incrementally refined. We evaluate
our representation along three axes: (1). compression, (2). denoising
capability, and (3). image completion capability. To assess these axes, we
consider the tasks of image fitting, 3D fitting, and novel view synthesis,
where our method shows an improved performance compared to state-of-the-art
tensor-based methods. For full results see our project webpage:
this https URL

我们提出了一种名为 'Prolongation Upsampling Tensor Train (PuTT)' 的新方法，通过延长学习到的张量列车表示来学习压缩、去噪和图像完整性能力，得到了比现有方法更好的性能。