Abstract
In this paper, we propose a novel non-convex tensor rank surrogate function and a novel non-convex sparsity measure for tensor. The basic idea is to sidestep the bias of $\ell_1-$norm by introducing concavity. Furthermore, we employ the proposed non-convex penalties in tensor recovery problems such as tensor completion and tensor robust principal component analysis, which has various real applications such as image inpainting and denoising. Due to the concavity, the models are difficult to solve. To tackle this problem, we devise majorization minimization algorithms, which optimize upper bounds of original functions in each iteration, and every sub-problem is solved by alternating direction multiplier method. Finally, experimental results on natural images and hyperspectral images demonstrate the effectiveness and efficiency of the proposed methods.
Abstract (translated)
本文提出了一种新的非凸张量秩代理函数和一种新的张量非凸稀疏测度。其基本思想是通过引入凹度来回避$ell_1-$norm的偏见。此外，在张量完备和张量鲁棒主成分分析等张量恢复问题中，我们还采用了所提出的非凸惩罚，这两个问题具有多种实际应用，如图像的修复和去噪。由于模型的凹性，很难求解。为了解决这个问题，我们设计了优化最小化算法，在每次迭代中优化原始函数的上界，并用交替方向乘法器法求解每个子问题。最后，对自然图像和高光谱图像的实验结果证明了该方法的有效性和有效性。
URL
https://arxiv.org/abs/1904.10165
