Hyperspectral images (HSI) can be naturally viewed as a third-order tensor with strong correlations between various dimensions. Thus, tensor-based methods are better than vector-based or matrix-based methods on exploiting the underlying structural information of the HSIs. However, existing HSI compressed sensing reconstruction (HSI-CSR) methods cann't sufficiently utilize this internal underlying structure of HSI. Thus, we propose a new method for HSI-CSR, namely multimode low-rank tensor approximation combining spatial-spectral pixel-wise smoothness constraints (MLRTAS). Firstly, a series of fourth-order tensors are constructed to well preserve the intrinsic structure of the HSIs. Then the correlation in each dimension of the constructed tensor is explored based on tensor multimodal non-convex low-rank regularization, which could make efficient use of the tensor spatial-spectral joint correlation as well as local and nonlocal self-similarity of the HSIs. Meanwhile, the reconstruction model is further constrained by the spatial-spectral pixel-wise smoothness of the HSI. The two regularizations are integrated into the reconstruction model and formulated as a non-convex optimization problem. Finally, an iterative optimization algorithm is developed to solve the model and reconstruct the HSIs. Extensive experiments on various public hyperspectral datasets show that our proposed method can significantly outperform existing HSI-CSR methods both in visual and numerical comparisons.

中文翻译：

---

通过张量多模低阶先验和空间光谱平滑正则化恢复高光谱图像

高光谱图像（HSI）可以自然地被视为在各个维度之间具有很强相关性的三阶张量。因此，在利用 HSI 的底层结构信息方面，基于张量的方法比基于向量或基于矩阵的方法更好。然而，现有的HSI压缩感知重建（HSI-CSR）方法无法充分利用HSI的这种内部底层结构。因此，我们提出了一种 HSI-CSR 的新方法，即结合空间谱像素平滑度约束的多模低秩张量近似（MLRTAS）。首先，构造一系列四阶张量以很好地保留 HSI 的内在结构。然后基于张量多模态非凸低秩正则化探索所构造张量各个维度的相关性，可以有效利用张量空间-谱联合相关性以及HSI的局部和非局部自相似性。同时，重建模型进一步受到 HSI 的空间光谱像素平滑度的限制。这两个正则化被集成到重建模型中并被表述为非凸优化问题。最后，开发了迭代优化算法来求解模型并重建 HSI。对各种公共高光谱数据集的大量实验表明，我们提出的方法在视觉和数值比较方面都可以显着优于现有的 HSI-CSR 方法。