Frequency-Weighted Robust Tensor Principal Component Analysis

Robust tensor principal component analysis (RTPCA) can separate the low-rank component and sparse component from multidimensional data, which has been used successfully in several image applications. Its performance varies with different kinds of tensor decompositions, and the tensor singular value decomposition (t-SVD) is a popularly selected one. The standard t-SVD takes the discrete Fourier transform to exploit the residual in the 3rd mode in the decomposition. When minimizing the tensor nuclear norm related to t-SVD, all the frontal slices in frequency domain are optimized equally. In this paper, we incorporate frequency component analysis into t-SVD to enhance the RTPCA performance. Specially, different frequency bands are unequally weighted with respect to the corresponding physical meanings, and the frequency-weighted tensor nuclear norm can be obtained. Accordingly we rigorously deduce the frequency-weighted tensor singular value threshold operator, and apply it for low rank approximation subproblem in RTPCA. The newly obtained frequency-weighted RTPCA can be solved by alternating direction method of multipliers, and it is the first time that frequency analysis is taken in tensor principal component analysis. Numerical experiments on synthetic 3D data, color image denoising and background modeling verify that the proposed method outperforms the state-of-the-art algorithms both in accuracy and computational complexity

Non-Convex Tensor Low-Rank Approximation for Infrared Small Target Detection

Infrared small target detection is an important fundamental task in the infrared system. Therefore, many infrared small target detection methods have been proposed, in which the low-rank model has been used as a powerful tool. However, most low-rank-based methods assign the same weights for different singular values, which will lead to inaccurate background estimation. Considering that different singular values have different importance and should be treated discriminatively, in this paper, we propose a non-convex tensor low-rank approximation (NTLA) method for infrared small target detection. In our method, NTLA regularization adaptively assigns different weights to different singular values for accurate background estimation. Based on the proposed NTLA, we propose asymmetric spatial-temporal total variation (ASTTV) regularization to achieve more accurate background estimation in complex scenes. Compared with the traditional total variation approach, ASTTV exploits different smoothness intensities for spatial and temporal regularization. We design an efficient algorithm to find the optimal solution of our method. Compared with some state-of-the-art methods, the proposed method achieves an improvement in terms of various evaluation metrics. Extensive experimental results in various complex scenes demonstrate that our method has strong robustness and low false-alarm rate. Code is available at https://github.com/LiuTing20a/ASTTV-NTLA.Comment: This paper is accepted by IEEE Transactions on Geoscience and Remote Sensin