Compressive sensing (CS) of high-order data such as hyperspectral images, medical imaging, video sequences, and multi-sensor networks is certainly a hot issue after the emergence of tensor decomposition. Actually, the reconstruction accuracy with current algorithms is not ideal in some cases of noise. In this paper, we propose a new method that can recover noisy 3-D images from a reduced set of compressive measurements. First, multi-way compressive measurements are performed using Gaussian random matrices. Second, the mapping relationship between the variance of noise and the reconstruction threshold is found. Finally, the original images are recovered through reconstruction of pseudo inverse based on threshold selection. We experimentally demonstrate that the proposed method outperforms other similar methods in both reconstruction accuracy (within a range of the compression ratios and different variances of noise) and processing speed.

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