基于FOCUSS改进算法的图像稀疏重构  

Image sparse reconstruction based on improved FOCUSS algorithm

作　　者：祝勇俊[1] 刘文波[1] 郑祥爱 沈骞[1] Zhu Yongjun;Liu Wenbo;Zheng Xiang'ai;Shen Qian(College of Automation Engineering,Nanjing University of Aeronautics and Astronautics,Nanjing 211106,China)

机构地区：[1]南京航空航天大学自动化学院,南京211106

出　　处：《电子测量技术》2020年第4期126-131,共6页Electronic Measurement Technology

基　　金：国家重点研发计划(2018YFB2003304);国家自然科学基金项目(61871218)资助。

摘　　要：分析分块压缩感知的基础上,提出了基于欠定系统局灶解法和L-曲线优化相结合的图像重构方法。利用灰度空间相关矩阵获知图像的纹理结构和优化块向量生成,噪声卡方分布设置拉格朗日乘子λ的阈值范围,采用4阶曲线拟合和最大曲率点拟合相结合方式确定λ的优化值,并设置双误差迭代停止方式来改进基础局灶算法。对比实验表明,基于L1范数最小化下的欠定系统局灶改进算法在无噪声和有噪声条件下都能改善图像重构,且性能优于传统的正交匹配算法和基追踪算法,同时该改进算法对不同图像具有一定的普适性。Based on the analysis of block compression sensing(BCS), an image reconstruction method is proposed by combination of focal underdetermined system solution(FOCUSS) and L-curve optimization. The gray-scale spatial correlation matrix is used to obtain the texture structure of the image and generate the optimized block vector. The noise chi-square distribution helps the setting of the threshold range of the Lagrange multiplier λ, and the combination of the fourth-order curve fitting and the maximum curvature point fitting is used to determine the optimal value of λ. In addition, double error iteration stop method is adopted to improve the basic FOCUSS algorithm. The contrast experiments show that the modified FOCUSS algorithm based on L1 norm minimization can improve image reconstruction under both noiseless and noisy conditions, and has better performance than the traditional orthogonal matching algorithm and base pursuit algorithm. Furthermore,the modified algorithm has a certain universality for different images.

关 键 词：欠定系统局灶解法 L-曲线 纹理结构 卡方分布 双误差 

分 类 号：TP2[自动化与计算机技术—检测技术与自动化装置]