利用期望-最大化算法实现基于动态词典的压缩感知

An EM-based Approach for Compressed Sensing Using Dynamic Dictionaries

在现有压缩感知(CS)理论中,重构信号需要预设其稀疏表示词典。对于以参数化模型表示的信号,只能预知该词典为某种形式的参数化词典,参数的具体取值难以确定。若将参数设定为取值空间的均匀离散格点,预设词典与真实词典之间的失配将使传统CS重构方法的性能严重恶化。为解决这一问题,该文提出一种基于动态词典的CS重构方法。通过迭代地优化词典参数,该方法在信号重构过程中对词典进行动态调整。为同时实现稀疏恢复与词典调整,该方法利用变分期望-最大化(EM)算法交替执行信号系数估计与词典参数优化。实验结果表明所提方法是有效的。

In the current Compressed Sensing （CS） theory, signal reconstruction depends on presetting an appropriate sparsifying dictionary. For signals characterized by parametric models, this dictionary is known to be a parameterized dictionary of a certain form, but the values of the parameters are difficult to determine. If the parameters are set to a group of uniform grid points, the mismatch between the assumed and the actual sparsifying dictionaries will cause the performance of conventional CS reconstruction methods to degrade considerably. To address this, a CS reconstruction method that utilizes dynamic dictionaries is proposed. By iteratively optimizing dictionary parameters, the method refines the dictionary dynamically during signal reconstruction. To achieve joint sparse recovery and dictionary refinement, the method alternates between steps of signal coefficients estimation and dictionary parameters optimization under the framework of the variational Expectation-Maximization （EM） algorithm. Experimental results demonstrate the effectiveness of the proposed method.