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基于改进的后退型最优正交匹配追踪的图像重建方法
引用本文:方红,章权兵,韦穗.基于改进的后退型最优正交匹配追踪的图像重建方法[J].华南理工大学学报(自然科学版),2008,36(8).
作者姓名:方红  章权兵  韦穗
作者单位:1. 合肥工业大学,理学院,安徽,合肥,230009
2. 安徽大学,计算智能与信号处理教育部重点实验室,安徽,合肥,230039
摘    要:摘要:正交匹配追踪OMP(Orthogonal Matching Pursuit)是可压缩传感理论CS(Compressed Sensing)中一种贪婪迭代的图像重建方法,该方法以快速高效而著称。但现有的OMP算法都是在给定迭代次数(待重建图像的稀疏度)的条件下重建,这样强制迭代过程停止的方法使得OMP方法需要非常多的线性测量来保证精确重建。本文提出一种改进的后退型最优OMP算法。该方法首先利用最优正交匹配追踪OOMP (Optimized Orthogonal Matching Pursuit)算法,在迭代过程通过最优的正交化性来约束原子的选择,保证原子的选择在最小化当前冗余误差的意义下最优;利用稀疏度作为适应性迭代次数的标准,给出一种非常简单的原子选择机制对得到的迭代结果进行后处理,向后剔除其中多余的原子从而获得精确重建。实验结果表明,与OMP相比较,改进算法可以获得精确重建并大大降低了对测量数目的要求。

关 键 词:关键词:正交匹配追踪  可压缩传感  稀疏    
收稿时间:2007-6-6
修稿时间:2007-8-9

Image Reconstruction Based on Improved Backward Optimized Orthogonal Matching Pursuit Algorithm
Fang Hong,Zhang Quan-bing,Wei Sui.Image Reconstruction Based on Improved Backward Optimized Orthogonal Matching Pursuit Algorithm[J].Journal of South China University of Technology(Natural Science Edition),2008,36(8).
Authors:Fang Hong  Zhang Quan-bing  Wei Sui
Abstract:Abstract: Orthogonal Matching Pursuit is a greedy and iterative method for image reconstruction of Compressed Sensing. Within all kinds of reconstruction methods, OMP is one of the most efficient algorithms. But existing OMP algorithms acquire reconstruction with the given number of iteration, i.e, the level of sparsity of the image to reconstruct, which makes OMP need more linear measurements to ensure accuracy. An improved OMP algorithm is presented. By the Optimized Orthogonal Matching Pursuit, we adopt optimized orthogonality to restrict the selection of atoms during iteration to minimize the norm of the corresponding residual error. Then with the level of sparsity as the standard of the adaptive iteration number, we present a very simple principle of atom selection for post disposing the final iteration result, which backward eliminates superfluous atoms to acquire exact reconstruction. Experimental results show that compared with OMP, the improved algorithm can acquire exact reconstruction and greatly reduce the requirement of the number of measurements.
Keywords:Keywords: Orthogonal Matching Pursuit  Compressed Sensing  Sparsity
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