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首页> 外文期刊>Neural Networks and Learning Systems, IEEE Transactions on >Robust Image Regression Based on the Extended Matrix Variate Power Exponential Distribution of Dependent Noise
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Robust Image Regression Based on the Extended Matrix Variate Power Exponential Distribution of Dependent Noise

机译：基于相依噪声的扩展矩阵变量幂指数分布的鲁棒图像回归

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摘要

Dealing with partial occlusion or illumination is one of the most challenging problems in image representation and classification. In this problem, the characterization of the representation error plays a crucial role. In most current approaches, the error matrix needs to be stretched into a vector and each element is assumed to be independently corrupted. This ignores the dependence between the elements of error. In this paper, it is assumed that the error image caused by partial occlusion or illumination changes is a random matrix variate and follows the extended matrix variate power exponential distribution. This has the heavy tailed regions and can be used to describe a matrix pattern of dimensional observations that are not independent. This paper reveals the essence of the proposed distribution: it actually alleviates the correlations between pixels in an error matrix E and makes E approximately Gaussian. On the basis of this distribution, we derive a Schatten -norm-based matrix regression model with regularization. Alternating direction method of multipliers is applied to solve this model. To get a closed-form solution in each step of the algorithm, two singular value function thresholding operators are introduced. In addition, the extended Schatten -norm is utilized to characterize the distance between the test samples and classes in the design of the classifier. Extensive experimental results for image reconstruction and classification with structural noise demonstrate that the proposed algorithm works much more robustly than some existing regression-based methods.
机译：处理局部遮挡或照明是图像表示和分类中最具挑战性的问题之一。在这个问题中，表征误差的表征起着至关重要的作用。在大多数当前方法中，需要将误差矩阵扩展为一个向量，并假设每个元素都被独立破坏。这忽略了错误元素之间的依赖性。在本文中，假设由部分遮挡或照明变化引起的误差图像是随机矩阵变量，并且遵循扩展矩阵变量幂指数分布。它具有较重的尾部区域，可用于描述非独立的维数观测的矩阵模式。本文揭示了提出的分布的本质：它实际上减轻了误差矩阵E中像素之间的相关性，并使E近似为高斯分布。在此分布的基础上，我们推导了基于Schatten范数的带有正则化的矩阵回归模型。采用乘数交替方向法求解该模型。为了在算法的每个步骤中获得封闭形式的解决方案，引入了两个奇异值函数阈值运算符。此外，在分类器的设计中，扩展的Schatten-norm用于表征测试样本与类之间的距离。带有结构噪声的图像重建和分类的大量实验结果表明，与现有的一些基于回归的方法相比，所提出的算法具有更强的鲁棒性。

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