论文部分内容阅读
在对信号稀疏性统计分析的基础上,将具有稀疏描述能力的拉普拉斯分布用于描述信号的先验分布,基于贝叶斯法,利用信号采样值、拉普拉斯先验分布和高斯似然模型,推导信号的后验概率密度估计;最后将最大后验概率(MAP)估计过程转化为加权迭代L1范数的最小化问题。在求解过程中,与非加权的L1范数法进行对比表明,信号重构性能明显提高;通过实验计算,详细讨论了其中一些参数的取值原则和范围;针对稀疏度不同的信号,随着信号非零点数的增加,本文算法重构结果明显优于基追踪(BP)和(OMP)法;与同类的IRL1算法相比较,本文算法更具普遍性和理论意义。
Based on the statistical analysis of signal sparsity, the Laplacian distribution with sparse description ability is used to describe the prior distribution of signals. Based on Bayesian method, the signal samples, Laplacian prior distribution and Gaussian likelihood model to derive the posterior probability density estimation of the signal. Finally, the maximum a posteriori probability (MAP) estimation process is transformed into the weighted iteration L1 norm minimization problem. In the process of solving, the comparison with the non-weighted L1 norm method shows that the signal reconstruction performance is obviously improved. The principles and scope of the values of some of these parameters are discussed in detail through experiments. For signals with different sparsity, Signal non-zero points increase, the results of the reconstruction algorithm is obviously better than the base pursuit (BP) and (OMP) algorithm; Compared with similar IRL1 algorithm, the algorithm in this paper is more universal and theoretical.