基于非局部相似及加权截断核范数的高光谱图像去噪

Hyperspectral Image Denoising Based on Non-local Similarity and Weighted-truncated Nuclear Norm

受仪器噪声干扰,高光谱图像(Hyperspectral Image,HSI)往往会受到高斯噪声的破坏,严重影响图像后续处理的精度,因此图像去噪是一项重要的预处理工作。此外,由于高光谱数据维度极高,因此算法效率成为模型应用能力的重要指标。为实现高效HSI去噪,文中首先将高维高光谱图像投影到低维光谱子空间上,从中学习一个正交基矩阵,然后结合高光谱的空间非局部相似性与全局光谱低秩性对低维子空间进行去噪,最后将复原后的低维图像与正交基结合恢复成原始数据维度。其中,非局部去噪过程要先通过图像的非局部相似性以邻域匹配方法寻找相似张量块组成具有强低秩属性的张量群组。针对各张量群组,文章联合加权核范数与截断核范数各自的优势,提出加权截断核范数作为低秩约束正则项,能更好地逼近本质秩属性。进一步,为快速获取模型的最优解,提出改进的近端加速梯度(Accelerated Proximal Gradient,APG)算法对低秩项进行优化求解。通过两组高光谱图像和一组多光谱图像对所提算法进行实验验证,结果表明,所提方法在视觉效果和时间效率上取得了良好的平衡,综合性能明显优于其他基于非局部去噪的对比算法。

Due to the interference of instrumental noise,hyperspectral images(HSI)are often corrupted to some extent by Gaussian noise,which will seriously affect the subsequent performance of image processing.Therefore,image denoising has been considered as an important pre-processing step.Besides,due to the high dimensionality of hyperspectral data,the running efficiency is also a critical factor along with the visual evaluation.For the sake of improving both the efficiency and efficacy,we first project the high-dimensional hyperspectral image into certain spectral subspace,and then learn an orthogonal basis matrix.On that basis,the spatial non-local similarity and the global spectral low rank property of hyperspectral are jointly introduced to denoise the low-dimensional subspaces.Finally,all the restored low-dimensional image can be used along with the orthogonal basis to recover the original HIS data.Among these steps,the non-local denoising process first forms certain amount of tensor cubes by the non-local similarity,and followed by several tensor groups using the block matching method.In general,these groups enjoy strong low-rank essense due to the explicit neighborhood similarity.For better revealing the low-rank property of each tensor group,we propose a weighted and truncated nuclear norm by taking both the advantages of weighted nuclear norm and truncated nuclear norm.Moreover,an improved optimization scheme based on the accelerated proximal gradient is presented for a fast solution.Extensive simulation results show that our denoising scheme outperforms state-of-the-art methods in objective metrics and better preserves visually salient structural features.