基于稀疏补分析模型的近似最优子空间追踪

为了从含噪声的测量矢量中重构原始信号，研究了稀疏补分析模型下近似最优子空间追踪信号重构算法.针对直接采用稀疏综合模型下子空间追踪过程非最速梯度下降和信号重构概率不高的缺点，根据稀疏补分析模型下不同类型分析字典的结构特点来设计近似目标优化函数；改进了迭代追踪过程；优化了稀疏补取值方法；提出并实现了基于稀疏补分析模型的近似最优分析子空间追踪算法.仿真实验证明，当稀疏补运算符分别采用随机紧支框架和二维全变分矩阵时，算法的完全重构信号概率均明显高于ASP、AHTP、AIHT、AL1、GAP算法的完全重构信号概率；对于含高斯噪声的输入信号，算法的重构信号综合平均PSNR比相应的ASP、AHTP、AIHT算法分别提高了0.8dB、1.38dB、3.13 dB，但比GAP和AL1算法降低了0.32 dB和0.6dB.算法的完全重构概率与综合重构性能有了明显提高，收敛充分条件得到进一步简化.

Approxi mately Opti mal Subspace Pursuit Based on Cosparse Analysis Model

An approximately optimal subspace pursuit algorithm under cosparse analysis model was studied to recon-struct the original signal from the noisy measurement vectors.To overcome the drawbacks of the non steepest gradient during the pursuit process and the low successful reconstruction probability for sparse synthesis model,an approximately optimal sub-space pursuit algorithm based on cosparse analysis model was presented and realized.The approximately optimal optimization object function for the algorithm was designed according to the structure of the different analysis dictionaries,the iterative pur-suit process of the algorithm was revised,and the methods of selecting cosparsity was optimized.The simulation experiments show that the complete reconstruction probability of the new algorithm is evidently larger than that of the algorithm for ASP, AHTP,AIHT,AL1 and GAP when the cosparse operator is a random compact frame or a two dimension total variant matrix. The comprehensive average PSNR of the output signal for the new algorithm is larger than that of the algorithm of ASP, AHTP,and AIHT for 0. 8dB,1. 38dB and 3. 13 dB respectively and is less than that of the algorithm of GAP and AL1 for 0. 32 dB and 0. 6dB when the input signal is with Gaussion noise.The complete reconstruction probability of the new algorithm was greatly improved by adopting the above measures,and the convergence condition for the new algorithm was simplified.