A Stochastic Gradient Approach on Compressive Sensing Signal Reconstruction Based on Adaptive Filtering Framework
A Stochastic Gradient Approach on Compressive Sensing Signal Reconstruction Based on Adaptive Filtering Framework
复制标题
基于自适应滤波框架的压缩感知信号重建随机梯度法
DOI：
10.1109/jstsp.2009.2039173
复制
发表时间：
2010-04-01
影响因子：
7.5
通讯作者：
Mei, Shunliang
中科院分区：
文献类型：
--
作者：
Jin, Jian;Gu, Yuantao;Mei, Shunliang
基于稀疏信号重构与系统辨识方法的相似性，提出了一种新的压缩感知（CS）稀疏信号重构方法。该方法采用了一种基于随机梯度的自适应滤波框架，这是常用的系统识别，解决稀疏信号重建问题。本文介绍了两种典型的算法：<sub>10</sub>-最小均方（<sub>10</sub>-LMS）算法和<sub>10</sub>-指数遗忘窗LMS（<sub>10</sub><i></i><i></i><i></i><i></i>这两种算法都利用了零吸引力的方法，这已经实现了通过最小化的连续近似的<i>l</i><sub>0</sub>范数的研究信号。为了提高这些算法的性能，还采用了一种<sub>l0</sub>-zero吸引投影（<sub>l0</sub>-ZAP）算法，有效地加快了它们的收敛速度，使它们比现有的其他算法更快。<i></i><i></i>所提出的方法的优点，例如其对噪声的鲁棒性等，通过数值实验证明。
Based on the methodological similarity between sparse signal reconstruction and system identification, a new approach for sparse signal reconstruction in compressive sensing (CS) is proposed in this paper. This approach employs a stochastic gradient-based adaptive filtering framework, which is commonly used in system identification, to solve the sparse signal reconstruction problem. Two typical algorithms for this problem: <i>l</i> <sub>0</sub>-least mean square ( <i>l</i> <sub>0</sub>-LMS) algorithm and <i>l</i> <sub>0</sub>-exponentially forgetting window LMS (<i>l</i> <sub>0</sub>-EFWLMS) algorithm are hence introduced here. Both the algorithms utilize a zero attraction method, which has been implemented by minimizing a continuous approximation of <i>l</i> <sub>0</sub> norm of the studied signal. To improve the performances of these proposed algorithms, an <i>l</i> <sub>0</sub>-zero attraction projection (<i>l</i> <sub>0</sub> -ZAP) algorithm is also adopted, which has effectively accelerated their convergence rates, making them much faster than the other existing algorithms for this problem. Advantages of the proposed approach, such as its robustness against noise, etc., are demonstrated by numerical experiments.