Collaborative sparse regression using spatially correlated supports - Application to hyperspectral unmixing
Collaborative sparse regression using spatially correlated supports - Application to hyperspectral unmixing
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DOI：
10.1109/tip.2015.2487862
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发表时间：
2014-09
影响因子：
10.6
通讯作者：
Y. Altmann;M. Pereyra;J. Bioucas-Dias
中科院分区：
文献类型：
--
作者：
Y. Altmann;M. Pereyra;J. Bioucas-Dias
本文提出了一种新的贝叶斯协作稀疏回归方法，用于高光谱图像的线性分解。我们的贡献是双重的；首先，我们提出了一种用于结构化稀疏回归的新贝叶斯模型，其中稀疏丰度向量的支持是跨像素先验空间相关的（即，材料是空间组织的，而不是在像素级别随机分布的）。该先验信息通过截断的多元伊辛马尔可夫随机场在模型中进行编码，该随机场还考虑了像素不能为空（即每个像素中至少存在一种材料）以及不同材料可能表现出不同程度的空间规律性的事实。其次，我们提出了一种先进的马尔可夫链蒙特卡罗算法来估计每个像素中材料存在或不存在的后验概率，并且以支持的最大边际后验配置为条件，计算丰度向量的最小均方误差估计。该算法的一个显着特性是它可以自我调整马尔可夫随机场的参数值，从而使从业者无需通过交叉验证来设置正则化参数。通过一系列合成数据和真实数据的实验以及与文献中其他算法的比较，最终证明了所提出方法的性能。
This paper presents a new Bayesian collaborative sparse regression method for linear unmixing of hyperspectral images. Our contribution is twofold; first, we propose a new Bayesian model for structured sparse regression in which the supports of the sparse abundance vectors are a priori spatially correlated across pixels (i.e., materials are spatially organized rather than randomly distributed at a pixel level). This prior information is encoded in the model through a truncated multivariate Ising Markov random field, which also takes into consideration the facts that pixels cannot be empty (i.e., there is at least one material present in each pixel), and that different materials may exhibit different degrees of spatial regularity. Second, we propose an advanced Markov chain Monte Carlo algorithm to estimate the posterior probabilities that materials are present or absent in each pixel, and, conditionally to the maximum marginal a posteriori configuration of the support, compute the minimum mean squared error estimates of the abundance vectors. A remarkable property of this algorithm is that it self-adjusts the values of the parameters of the Markov random field, thus relieving practitioners from setting regularization parameters by cross-validation. The performance of the proposed methodology is finally demonstrated through a series of experiments with synthetic and real data and comparisons with other algorithms from the literature.