Wu Yue, Fang Leyuan, Li Shutao
IEEE Trans Image Process. 2018 Dec 27. doi: 10.1109/TIP.2018.2889914.
Natural images often contain patches with high similarity. In this paper, to effectively utilize the local and nonlocal self-similarity for low-rank models, we propose a novel weighted tensor rank-1 decomposition method (terms as WTR1) for nonlocal image denoising. Although the low-rank approximation problem has been well studied for matrices, it remains elusive of the theoretically extension to tensors due to the NPhard tensor decomposition. To tackle this problem, the proposed WTR1 method designs a new efficient CANDECOMP/PARAFAC (CP) decomposition algorithm and constructs a straightforward low-rank tensor approximation strategy. This is achieved by elegantly manipulating the CP-rank, called intrinsic low-rank tensor approximation. Specifically, the WTR1 method first groups similar patches into a 3-D stack and converts the stack into a finite sum of rank-1 products. Then, we deploy the intrinsic low-rank tensor approximation to produce the final denoised image. The proposed WTR1 method can jointly exploit the local and nonlocal self-similarity, thus improving the nonlocal image denoising quality. Experimental results have shown that the proposed WTR1 outperforms several state-of-the-art denoising methods.
自然图像通常包含具有高度相似性的图像块。在本文中，为了在低秩模型中有效利用局部和非局部自相似性，我们提出了一种用于非局部图像去噪的新型加权张量秩 - 1分解方法（称为WTR1）。尽管低秩逼近问题在矩阵方面已经得到了充分研究，但由于NP难的张量分解问题，其在张量上的理论扩展仍然难以捉摸。为了解决这个问题，所提出的WTR1方法设计了一种新的高效的CANDECOMP/PARAFAC（CP）分解算法，并构建了一种直接的低秩张量逼近策略。这是通过巧妙地操纵CP秩来实现的，称为内在低秩张量逼近。具体来说，WTR1方法首先将相似的图像块分组为一个3D堆栈，并将该堆栈转换为秩 - 1乘积的有限和。然后，我们采用内在低秩张量逼近以生成最终的去噪图像。所提出的WTR1方法可以联合利用局部和非局部自相似性，从而提高非局部图像去噪质量。实验结果表明，所提出的WTR1方法优于几种现有的去噪方法。
