Hyperspectral Mixed Noise Image Restoration Based on Non-Convex Low-Rank Tensor Decomposition and Group Sparse Total Variation
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摘要:
高光谱图像（Hyperspectral Image，HSI）在采集的过程中会被大量混合噪声污染，会影响遥感图像后续应用的性能，因此从混合噪声中恢复干净的HSI成为了重要的预处理过程。在本文中，提出了一种基于非凸低秩张量分解和群稀疏总变分正则化的高光谱混合噪声图像恢复模型；一方面，采用对数张量核范数来逼近HSI的低秩特性，可以利用高光谱数据固有的张量结构，同时减少对较大奇异值的收缩以保留图像更多细节特征；另一方面，采用群稀疏总变分正则化来增强HSI的空间稀疏性和相邻光谱间的相关性。并采用ADMM（Alternating Direction Multiplier Method）算法求解，实验证明该算法易于收敛。在模拟和真实的高光谱图像实验中，与其他方法相比，该方法在去除HSI混合噪声方面具有更好的性能。
Abstract:Hyperspectral images (HSIs) are polluted by a large amount of mixed noise during the acquisition process, which affects the performance of subsequent applications of remote sensing images. Therefore, restoring clean HSI from the mixed noise is an important preprocessing step. In this study, a hyperspectral mixed noise image restoration model based on nonconvex low-rank tensor decomposition and group-sparse total variational regularization is proposed. On the one hand, by using logarithmic tensor nuclear norm to approximate the low-rank characteristics of the HSI, the inherent tensor structure of hyperspectral data can be utilized, and the shrinkage of larger singular values can be reduced to preserve more detailed features of the image. On the other hand, the group sparse total variational regularization can be used to enhance the spatial sparsity of the HSI and correlation between adjacent spectra. ADMM algorithm is used to solve the problem, and an experiment shows that the algorithm converges easily. In simulated and real hyperspectral image experiments, this method performs better in removing HSI mixed noise when compared to other methods.
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图 1 Case1中各种算法去噪后第20波段对比
Figure 1. Comparison of the 20th band after denoising of various algorithms in Case1
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图 2 Case2中各种算法去噪后第58波段对比
Figure 2. Comparison of the 58th band after denoising of various algorithms in Case2
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图 6 HYDICE Urban数据第109波段恢复图像比较
Figure 6. Comparison of restored images in the 109th band of HYDICE Urban data
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图 7 HYDICE Urban数据第109波段水平平均剖面比较
Figure 7. Comparison of the 109th band horizontal mean profile in HYDICE Urban data
表 1 Pavia city center数据集的不同去噪方法的定量评价结果
Table 1 Quantitative evaluation results of different denoising methods in Pavia city center data sets
Case Indexes Noise LRMR LRTV LRTDTV LRTDGS FRCTR-PnP NCLRGSTV Case 1 MPSNR 14.144 33.336 34.356 34.743 35.380 34.557 36.369 MSSIM 0.2143 0.9341 0.9444 0.9457 0.9506 0.9370 0.9637 MFSIM 0.5985 0.9590 0.9626 0.9646 0.9647 0.9630 0.9761 MSAM 0.6676 0.0833 0.0545 0.0495 0.0637 0.1331 0.0514 ERGAS 707.54 74.698 65.280 70.351 61.441 109.32 51.975 Time/s - 43.046 23.234 61.463 47.482 371.04 71.641 Case 2 MPSNR 14.118 33.175 34.291 34.710 35.294 34.251 36.232 MSSIM 0.2142 0.9332 0.9439 0.9457 0.9496 0.9348 0.9632 MFSIM 0.5976 0.9588 0.9627 0.9643 0.9710 0.9608 0.9757 MSAM 0.6687 0.0846 0.0547 0.0494 0.0625 0.1304 0.0519 ERGAS 707.93 75.787 65.678 61.582 59.506 108.85 52.485 Time/s - 43.294 22.994 61.906 44.786 397.41 72.997 Case 3 MPSNR 14.092 33.083 34.193 34.652 35.220 34.338 35.969 MSSIM 0.2114 0.9330 0.9437 0.9454 0.9491 0.9356 0.9619 MFSIM 0.5955 0.9587 0.9624 0.9641 0.9707 0.9618 0.9746 MSAM 0.6720 0.0855 0.0553 0.0493 0.0641 0.1207 0.0538 ERGAS 709.14 76.431 66.452 61.936 60.275 100.18 54.261 Time/s - 43.680 22.733 61.790 45.851 373.44 77.096 
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