论文标题
Riemannian信息梯度方法用于ECD的参数估计：图像处理中的某些应用
Riemannian information gradient methods for the parameter estimation of ECD: Some applications in image processing
论文作者
论文摘要
椭圆形的分布（ECD）在计算机视觉，图像处理，雷达和生物医学信号处理中起着重要作用。最大似然。 ECD的估计（MLE）导致了非线性方程的系统，最常用于使用定点（FP）方法来解决。不幸的是，对于大规模或高维数据集，这些方法所需的计算时间是不可接受的。为了克服这一困难，目前的工作引入了Riemannian优化方法，即信息随机梯度（ISG）。 ISG是一种在线（递归）方法，对于大规模数据集，它与MLE相同，同时需要适度的内存和时间资源。为了开发ISG方法，考虑到与ECD的基础参数空间相关的产品歧管，得出了Riemannian信息梯度。根据此信息梯度定义，我们还定义了信息确定性梯度（IDG），一个离线（批次）方法，是中等尺寸数据集的替代方法。目前的工作制定了这两种方法，并通过数值模拟证明了它们的性能。还制定了两个用于图像重新化和纹理分类的应用程序。
Elliptically-contoured distributions (ECD) play a significant role, in computer vision, image processing, radar, and biomedical signal processing. Maximum likelihood. estimation (MLE) of ECD leads to a system of non-linear equations, most-often addressed using fixed-point (FP) methods. Unfortunately, the computation time required for these methods is unacceptably long, for large-scale or high-dimensional datasets. To overcome this difficulty, the present work introduces a Riemannian optimisation method, the information stochastic gradient (ISG). The ISG is an online (recursive) method, which achieves the same performance as MLE, for large-scale datasets, while requiring modest memory and time resources. To develop the ISG method, the Riemannian information gradient is derived taking into account the product manifold associated to the underlying parameter space of the ECD. From this information gradient definition, we define also, the information deterministic gradient (IDG), an offline (batch) method, which is an alternative, for moderate-sized datasets. The present work formulates these two methods, and demonstrates their performance through numerical simulations. Two applications, to image re-colorization, and to texture classification, are also worked out.
