Under-Sampled High-Dimensional Data Recovery via Symbiotic Multi-Prior Tensor Reconstruction

TL;DR

This work tackles the challenge of recovering complete, high-dimensional data from under-sampled observations by introducing a symbiotic multi-prior tensor reconstruction framework. It fuses a learnable low-rank tensor decomposition, a pre-trained CNN-based local smoothing regularizer, and BM3D non-local similarity constraints within a constrained optimization solved by an ADMM scheme that decouples three interdependent priors. Key contributions include the novel integration of three priors, a practical ADMM solver with closed-form subproblem updates, and extensive validation across color images, hyperspectral imagery, and grayscale videos, particularly excelling at extreme sampling rates ($1\%$ to $5\%$). The proposed approach offers robust, scalable recovery for under-sampled high-dimensional data, with potential impact on multimedia, remote sensing, and sensing systems where data loss is common.

Abstract

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.

Figures (6)

• Figure 1: The three types of prior are symbiotic with each other.
• Figure 2: Comparison of reconstruction details in the reconstructed data using different methods for color image Baboon (first row, SR=20%), hyperspectral image Balloons (second row, SR=3%) and grayscale video Suzie (third row, SR=1%)
• Figure 3: PSNR and SSIM values with respect to the frame/band number of the recovered (a)(c) hyperspectral image Balloons and (b)(d) grayscale video Suzie by different methods.
• Figure 4: The pixel values along the temporal dimensional (the same location of each frame) of the recovered (a)(b) hyperspectral image Balloons and (c)(d) grayscale video Suzie.
• Figure 5: Effect of different smoothing intensities on the reconstruction quality for (a) color image House, (b) hyperspectral image Toy and (c) grayscale video Suzie.