利用概率结构稀疏模型实现信号重构的新算法

doi:10.3969/j.issn.1001-2400.2013.02.031

J4 ›› 2013, Vol. 40 ›› Issue (2): 194-200.doi: 10.3969/j.issn.1001-2400.2013.02.031

利用概率结构稀疏模型实现信号重构的新算法

何宜宝;毕笃彦

(空军工程大学工程学院，陕西西安 710038)

收稿日期:2011-12-02 出版日期:2013-04-20 发布日期:2013-05-22
通讯作者: 何宜宝
作者简介:何宜宝(1985-)，男，空军工程大学博士研究生，E-mail: gudujianboboo@yahoo.com.cn．
基金资助:
国家自然科学基金资助项目(61175029);国家部委科技重点实验室基金资助项目(9140c610301080c6106, 9140c6001070801);航空科学基金资助项目(20115896022)

Signal reconstruction algorithm based on the probabilistic structured sparse model

HE Yibao;BI Duyan

(School of Eng., Air Force Eng. Univ., Xi'an 710038， China)

Received:2011-12-02 Online:2013-04-20 Published:2013-05-22
Contact: HE Yibao

摘要/Abstract

摘要：

为更好地描述信号的结构稀疏性，构造了一种概率结构稀疏模型，并用于压缩感知信号重构问题．在对结构稀疏模型分析的基础上，不直接对信号的结构稀疏性进行描述，而是利用玻耳兹曼分布对其支撑的结构稀疏性进行先验描述，然后基于贝叶斯压缩感知理论，通过该先验分布和观测过程的高斯似然性，由观测值和观测矩阵求解信号支撑的最大后验估计，最后由信号支撑求解原信号．实验结果表明，对于已知信号支撑的稀疏信号，该方法重构性能明显优于BP和OMP法;对于一般的稀疏高斯随机信号，在高观测噪声水平和低重构误差容限条件下，其重构性能具有较大优势．

关键词: 压缩感知, 结构稀疏模型, 信号支撑, 玻耳兹曼分布

Abstract:

In order to describe structured sparsity of the signal accurately, a probabilistic structured sparse model is constructed for signal reconstruction in compressive sensing(CS). Based on the structured sparse model, Boltzmann distribution is introduced to describe structured sparsity of the signal support rather than to describe the signal directly. Based on Bayesian CS, the maximum a posterior estimate of signal support is computed with the prior distribution and the Gaussian likelihood model of measurement, and then the signal is reconstructed using signal support. Experimental results show that, for the signal with the support known, the proposed algorithm is obviously superior to BP and OMP and that for the signal with the support unknown, its performance outperforms that of BP and OMP in the condition of a high measurement noise level and low reconstruction error tolerance.

Key words: compressive sensing, structured sparse model, signal support, Boltzmann distribution

何宜宝;毕笃彦. 利用概率结构稀疏模型实现信号重构的新算法[J]. J4, 2013, 40(2): 194-200.

HE Yibao;BI Duyan. Signal reconstruction algorithm based on the probabilistic structured sparse model[J]. J4, 2013, 40(2): 194-200.

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利用概率结构稀疏模型实现信号重构的新算法

Signal reconstruction algorithm based on the probabilistic structured sparse model

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