针对低分辨率遥感影像空间分辨率提升问题,提出一种基于在线变分贝叶斯期望最大化耦合字典学习的单幅遥感影像超分辨率重建算法。该方法首先建立字典原子及各参数的概率分布模型,将其划分为局部变量及全局变量,并使用固定其他参数来更新当前参数的Gibbs抽样方法对各变量赋予初始值,然后采用随机优化方法对两类变量进行期望最大化(EM)迭代优化,通过最小化Kullback-Leibler(KL)距离来获取字典原子的后验分布,并对字典大小进行非参数推导。最后在重建阶段采用双边滤波将待重建影像分为平滑部分和纹理部分,对平滑部分采用双三次插值重建,而对纹理部分进行稀疏重建。对比双线性、双三次插值及基于稀疏表示的超分辨率重建方法,该算法在平均峰值信噪比方面分别提高了3.85,2.11,0.20 dB,在平均相对整体维数综合误差(ERGAS)方面分别降低了0.64,0.28,0.04 dB。实验结果表明该算法因加入了更多的样本和参数先验信息,可以使重建影像提供更多高频细节信息,具有一定的普适性及较强的噪声稳健性,且重构速度较快。

A single remote sensing image super-resolution reconstruction method based on online variational Bayes expectation maximization coupled dictionary learning is proposed in this study to improve the spatial resolution of low resolution remote sensing images. The method first establishes the probability distribution model of the dictionary atom and each parameter, divides it into local variables and global variables, and uses the Gibbs sampling method to update the current parameters with fixed other parameters to assign initial values to the variables. Then stochastic optimization method is used to optimize expectation maximization (EM) optimization for two kinds of variables. The posterior distribution of the dictionary atom is obtained by minimizing the Kullback-Leibler (KL) distance, and the dictionary size is derived non-parametrically. Finally, the image to be reconstructed is divided into smooth and texture patches by bilateral filter during reconstruction, the sparse reconstruction method is used for the texture part while the bicubic interpolation reconstruction is applied for the smooth part. Compared with the bilinear, the bicubic interpolation and the super-resolution reconstruction algorithm based on sparse representation, the average peak signal-to-noise ratios of the proposed method are increased by 3.85, 2.11, 0.20 dB, respectively. And the average relative global dimensional synthesis errors (ERGASs) are decreased by 0.64, 0.28, 0.04 dB, respectively. Experimental results show that this algorithm can provide more high-frequency detail information by adding more sample and parameter prior information, which has certain universality and strong noise robustness, and the reconstruction speed is faster.