Coarse-To-Fine Tensor Trains for Compact Visual Representations (2406.04332v1)

Abstract: 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: https://sebulo.github.io/PuTT_website/

• The paper introduces PuTT, a novel coarse-to-fine tensor train approach that incrementally refines visual representations to overcome local minima.
• The method achieves significant improvements, yielding over 2.5 PSNR and 0.1 SSIM gains on high-resolution images compared to CP and Tucker decompositions.
• By integrating Quantized Tensor Trains with a multigrid-inspired upsampling framework, PuTT advances applications in novel view synthesis and 3D reconstruction.

Coarse-To-Fine Tensor Trains for Compact Visual Representations

The paper "Coarse-To-Fine Tensor Trains for Compact Visual Representations" presents a novel methodology for optimizing tensor train representations intended to advance the capabilities in visual data applications such as novel view synthesis and 3D reconstruction.

Context and Motivation

Existing research has demonstrated the potential of tensor networks for compact and high-quality visual data representations. In particular, the application of tensor train (TT) decomposition has shown promise due to its efficient compression capabilities. However, the optimization of such tensor-based representations, specifically tensor trains, remains a significant challenge. This optimization difficulty limits the practical utility of tensor networks in visual data applications, as current methods often get stuck in local minima and struggle with noisy or incomplete data.

Proposed Method

The authors propose a Prolongation Upsampling Tensor Train (PuTT) method that leverages a coarse-to-fine learning strategy. This technique prolongs a learned tensor train representation by incrementally refining a sequence of tensor trains, starting from a coarse representation and progressively increasing detail. The coarse-to-fine framework utilizes prolongation operators, inspired by multigrid methods for solving partial differential equations, enabling efficient upsampling directly within the tensor train format. A unique aspect of this approach is its ability to handle Quantized Tensor Trains (QTT), which provide further compression efficiency through hierarchical structuring.

Evaluation and Results

The paper rigorously evaluates the proposed PuTT method on three axes: compression, denoising, and image completion capability. The experiments demonstrate superiority over existing state-of-the-art tensor-based methods across multiple tasks:

1. Compression: PuTT consistently outperforms baseline methods in both 2D and 3D data compression scenarios. For high-resolution images (e.g., 16k resolution), PuTT achieves an improvement of more than 2.5 in PSNR and 0.1 in SSIM compared to CP and Tucker methods.
2. Denoising: The method shows enhanced capability in denoising tasks. The model effectively mitigates the impact of noise, with significant improvements in both PSNR and SSIM over non-upsampling approaches.
3. Image Completion: In scenarios with missing data, PuTT demonstrates superior performance, effectively reconstructing missing data points in visual representations.

Novel View Synthesis

The application of PuTT to novel view synthesis further validates its utility. Compared to methods like TensoRF, particularly at high compression ratios, PuTT maintains or surpasses performance, delivering detailed visual reconstructions with lower memory requirements.

Theoretical and Practical Implications

Theoretically, the incorporation of Quantized Tensor Trains (QTT) within a coarse-to-fine framework substantiates the potential gains when dealing with hierarchical and multi-resolution data, especially in visual applications where fine details are paramount. Practically, the PuTT method offers a viable path for enhancing the efficiency and quality of tensor-based visual data representations.

Future Directions

The paper hints at several future developments. Firstly, extending the application of PuTT to large-scale Neural Radiance Fields (NeRFs) and dynamic neural fields could leverage the logarithmic dimensionality advantages of QTTs to represent large, finely detailed scenes. Additionally, exploring tensor rank increment strategies and further enhancing the optimization frameworks could lead to even more robust and efficient models.

Conclusion

By addressing the optimization challenges of tensor train representations, the proposed coarse-to-fine Prolongation Upsampling Tensor Train (PuTT) method marks a significant contribution to the field of visual data representation. Its application across compression, denoising, and image completion tasks converges towards achieving compact, high-quality, and storage-efficient representations, fueling advancements in computer vision and graphics applications. While current results are promising, future explorations into the theoretical underpinnings and practical enhancements will be crucial in harnessing the full potential of tensor train-based methods.