Hyperspectral images provide a rich representation of the underlying spectrum for each pixel, allowing for a pixel-wise classification/segmentation into different classes. As the acquisition of labeled training data is very time-consuming, unsupervised methods become crucial in hyperspectral image analysis. The spectral variability and noise in hyperspectral data make this task very challenging and define special requirements for such methods. Here, we present a novel unsupervised hyperspectral segmentation framework. It starts with a denoising and dimensionality reduction step by the well-established Minimum Noise Fraction (MNF) transform. Then, the Mumford-Shah (MS) segmentation functional is applied to segment the data. We equipped the MS functional with a novel robust distribution-dependent indicator function designed to handle the characteristic challenges of hyperspectral data. To optimize our objective function with respect to the parameters for which no closed form solution is available, we propose an efficient fixed point iteration scheme. Numerical experiments on four public benchmark datasets show that our method produces competitive results, which outperform three state-of-the-art methods substantially on three of these datasets.

翻译：超光谱图像为每个像素提供了丰富的深层光谱代表, 允许将标签培训数据分解/ 分解成不同的类别。 由于获取标签培训数据非常费时, 在超光谱图像分析中, 获取不受监督的方法变得至关重要。 超光谱数据的光谱变异性和噪音使得这项任务非常具有挑战性, 并界定了对这种方法的特殊要求 。 在这里, 我们提出了一个新的、 不受监督的超光谱分解框架 。 它首先通过完善的最小噪声分解( MNF) 转换, 开始一个分解和分解步骤 。 然后, Mumford- Shah (MS) 分解功能应用到数据分解部分 。 我们为MS 功能配备了一个新的、 强健健健的分布指标功能, 目的是处理超光谱数据的特殊挑战 。 为了在没有封闭式解决方案的参数上优化我们的目标功能, 我们建议一个高效的固定点的分解方案 。 在四个公共基准数据集上进行的数值实验显示我们的方法产生竞争性的结果, 大大超出这些数据集的三种状态的三种方法 。