通过融合多种先验信息，实现极低采样率下的高维数据恢复。
Under-Sampled High-Dimensional Data Recovery via Symbiotic Multi-Prior Tensor Reconstruction
- 结合可学习张量分解、预训练CNN和BM3D正则化，挖掘数据多维结构。
- 在超低采样率下仍能有效恢复彩色图像、高光谱图像与灰度视频。
- 适合处理传感器缺失、传输丢包等极端数据不完整场景。
传感技术的进步推动了高维数据的广泛应用，但采集与传输过程中的数据缺失严重影响后续任务精度。张量重建旨在通过挖掘高维数据的先验信息，从欠采样观测数据中恢复原始完整数据。然而，现有方法因先验探索不足，在极低采样率下仍面临挑战。本文提出一种融合多重先验的张量重建方法，综合使用可学习张量分解以施加低秩约束、预训练卷积神经网络进行平滑与去噪，以及块匹配与三维滤波正则化以增强重构数据的非局部相似性。设计交替方向乘子法将优化问题分解为三个子问题，高效求解。在彩色图像、高光谱图像及灰度视频数据集上的大量实验表明，该方法在极端低采样率下优于当前最先进方法。
原文摘要 · Abstract (English)
The advancement of sensing technology has driven the widespread application of high-dimensional data. However, issues such as missing entries during acquisition and transmission negatively impact the accuracy of subsequent tasks. Tensor reconstruction aims to recover the underlying complete data from under-sampled observed data by exploring prior information in high-dimensional data. However, due to insufficient exploration, reconstruction methods still face challenges when sampling rate is extremely low. This work proposes a tensor reconstruction method integrating multiple priors to comprehensively exploit the inherent structure of the data. Specifically, the method combines learnable tensor decomposition to enforce low-rank constraints of the reconstructed data, a pre-trained convolutional neural network for smoothing and denoising, and block-matching and 3D filtering regularization to enhance the non-local similarity in the reconstructed data. An alternating direction method of the multipliers algorithm is designed to decompose the resulting optimization problem into three subproblems for efficient resolution. Extensive experiments on color images, hyperspectral images, and grayscale videos datasets demonstrate the superiority of our method in extreme cases as compared with state-of-the-art methods.
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