参数自适应调整的稀疏贝叶斯重构算法

发布时间：2018-01-25 07:13

本文关键词： 压缩感知稀疏重构迭代重加权稀疏贝叶斯学习参数自动调整　出处：《电子与信息学报》2014年06期 　论文类型：期刊论文

【摘要】：稀疏表示模型中的正则化参数由未知的噪声和稀疏度共同决定,该参数的设置直接影响稀疏重构性能的好坏。然而目前稀疏表示问题优化求解算法或依靠主观、或依靠相关先验信息、或经过实验设置该参数,均无法自适应地设置调整该参数。针对这一问题,该文提出一种无需先验信息的参数自动调整的稀疏贝叶斯学习算法。首先对模型中各参数进行概率建模,然后在贝叶斯学习的框架下将参数设置及稀疏求解问题转化为一系列混合L1范数与加权L2范数之和的凸优化问题,最终通过迭代优化得到参数设置和问题求解。由理论推导和仿真实验可知,已知理想参数时,该算法与其它非自动设置参数的迭代重加权算法性能相当,甚至更优;在理想参数未知时,该算法的重构性能要明显优于其它算法。
[Abstract]:The regularization parameters in sparse representation model are determined by unknown noise and sparse degree. The setting of these parameters directly affects the performance of sparse reconstruction. Either depending on the prior information or setting the parameter through experiment, it can not set and adjust the parameter adaptively. In this paper, a sparse Bayesian learning algorithm is proposed, in which the parameters are automatically adjusted without prior information. Firstly, the probabilistic modeling of each parameter in the model is carried out. Then the problem of parameter setting and sparse solution is transformed into a series of convex optimization problems of the sum of mixed L1 norm and weighted L2 norm under the framework of Bayesian learning. Finally, the parameter setting and problem solving are obtained by iterative optimization. The theoretical derivation and simulation results show that the performance of the algorithm is equivalent to that of other iterative reweighting algorithms with non-automatic parameters when the ideal parameters are known. Even better; When the ideal parameters are unknown, the reconstruction performance of this algorithm is obviously better than that of other algorithms.
【作者单位】：电子工程学院;安徽省电子制约技术重点实验室;
【基金】：安徽省自然科学基金(1208085MF94,1308085QF99) 国家自然科学基金(61272333)资助课题
【分类号】：TN911.7
【正文快照】： 1引言近几年来,基于稀疏表示的机器学习方法在各领域得到迅速发展。将稀疏表示的思想引入解决机器学习的问题,最初是由压缩感知、稀疏表示在信号处理中的应用启发而来。两个问题可抽象为统一的稀疏重构问题来进行描述。稀疏重构任务可归结安徽省自然科学基金(1208085MF94,1308

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