张量分解和自适应图全变分的高光谱图像去噪

Hyperspectral image denoising based on tensor decomposition and adaptive weight graph total variation

高光谱图像在采集过程中受到观测条件、成像仪材料属性、传输条件等客观因素的影响,不可避免地会引入各种噪声。这严重降低了高光谱图像的质量以及限制了后续处理的精度。因此,高光谱图像去噪是一个极其重要的预处理步骤。针对高光谱图像去噪问题,提出了低秩张量分解和自适应图全变分的高光谱图像去噪算法。首先,利用低秩张量分解来描述高光谱图像的全局空间和光谱相关性,并使用自适应权重图全变分来刻画高光谱图像空间维度上的分段平滑特性和保留高光谱图像的边缘信息;此外,采用l1-范数、Frobenius-范数分别刻画包括条纹噪声、脉冲噪声、死线噪声在内的稀疏噪声和高斯噪声。由此高光谱图像去噪问题归结为一个包含低秩张量分解和自适应图全变分的约束优化问题。利用增广拉格朗日乘子法对该优化问题进行交替求解。实验结果表明,所提出的高光谱图像去噪算法与现有的算法相比,能够充分刻画高光谱图像数据的内在结构特性,具有更好的去噪性能。

During the acquisition process of hyperspectral images,various noises are inevitably introduced due to the influence of objective factors such as observation conditions,material properties of the imager,and transmission conditions,which severely reduces the quality of hyperspectral images and limits the accuracy of subsequent processing.Therefore,denoising of hyperspectral images is an extremely important preprocessing step.For the hyperspectral image denoising problem,a denoising algorithm,which is based on low-rank tensor decomposition and adaptive weight graph total variation regularization named LRTDGTV,is proposed in this paper.Specifically,Low-rank tensor decomposition is used to characterize the global correlation among all bands,and adaptive weight graph total variation regularization is adopted to characterize piecewise smoothness property of hyperspectral images in the spatial domain and preserve the edge information of hyperspectral images.In addition,sparse noise,including stripe noise,impulse noise and deadline noise,and Gaussian noise are characterized by l 1-norm and Frobenius-norm,respectively.Thus,the denoising problem can be formulated into a constrained optimization problem involving low-rank tensor decomposition and adaptive weight graph total variation regularization,which can be solved by employing the augmented Lagrange multiplier(ALM)method.Experimental results show that the proposed hyperspectral image denoising algorithm can fully characterize the inherent structural characteristics of hyperspectral images data and has a better denoising performance than the existing algorithms.