基于全变分加权差正则的高光谱图像去噪算法

针对现有全变分模型在高光谱图像中出现的伪影、边缘结构消失等问题, 文章提出一种增强型三维全变分加权差正则模型。首先, 该模型并非直接将稀疏性强加于梯度映射本身, 而是对梯度映射的基矩阵添加稀疏性约束。此外, 与一般稀疏约束方法不同的是, 为避免由 $ l_{1} $ 范数自身局限性带来的去噪不良影响, 利用 $ l_{1} $ 范数与 $ l_{2} $ 范数的全变分加权差(简记为 $ l_{1-2} $) 分别对高光谱图像的空间域与光谱域施加稀疏约束。实验结果表明, 该文提出的算法有效避免了伪影的产生以及图像细节丢失的问题, 具有更优的去噪效果。

Aiming at the problems of artifacts and edge structure disappearance in hyperspectral images of existing total variation models, an enhanced three-dimensional total variation weighted difference regularization model is proposed in this paper. Firstly, this model does not directly impose sparsity on the gradient map itself, but adds a sparsity constraint to the base matrix of the gradient map. In addition, different from the general sparsity constraint approaches, to avoid the undesirable effects of denoising caused by the limitations of the $ l_{1} $ norm, a sparse constraint is applied to the spatial domain and spectral domain of the hyperspectral image using the total variation weighted difference of $ l_{1} $ norm and $ l_{2} $ norm ( $ l_{1-2} $), respectively. Experimental results show that the proposed method effectively avoids artifacts and image details loss, and has a better denoising effect.