引用本文:刘连,王孝通.基于变分贝叶斯推断的字典学习算法[J].控制与决策,2020,35(2):469-473
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基于变分贝叶斯推断的字典学习算法
刘连,王孝通
(海军大连舰艇学院航海系,辽宁大连116018)
摘要:
传统的字典学习算法在对训练图像进行学习时收敛速率慢,当图像受到噪声干扰时学习效果变差.对此,提出一种基于变分推断的字典学习算法.首先设定模型中各参数的共轭稀疏先验分布;然后基于贝叶斯网络求出所有参数的联合概率密度函数;最后利用变分贝叶斯推断原理计算出各参数的最优边缘分布,训练出自适应学习字典.利用该字典进行图像去噪实验以及压缩感知重构实验,仿真结果表明,所提出的算法可显著提高字典学习效率,对测试图像的去噪效果和重构精度有很大改善.
关键词:  贝叶斯网络  变分推断  字典学习  图像去噪  压缩感知
DOI:10.13195/j.kzyjc.2018.0609
分类号:TN911.7
基金项目:国家自然科学基金项目(61471412, 61771020, 61373262).
Dictionary learning algorithm based on variable Bayes inference
LIU Lian,WANG Xiao-tong
(Department of Navigation,Dalian Naval Academy,Dalian 116018,China)
Abstract:
The traditional dictionary learning algorithms have slow convergence rate when learning the training image. And the effect of dictionary learning becomes worse if the images are corrupted by noise. Therefore, a dictionary learning algorithm based on variational inference is proposed to solve this problem. The algorithm firstly sets the conjugate sparse prior distribution of the parameters in the model, and then the joint probability density function of all parameters is calculated based on the Bayesian network. Finally, the optimal edge distribution of the parameters is calculated by the variational Bayesian inference, and the adaptive dictionary training is completed. The image denoising experiment and the compressed sensing image reconstruction experiment are carried out by the adaptive dictionary. The simulation results show that the algorithm can significantly increase the efficiency of dictionary learning, and the visual effect of the denoising and the reconstruction of the test images are improved.
Key words:  Bayesian network  variational inference  dictionary learning  image denoising  compressed sensing

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