改进的后退型最优正交匹配追踪图像重建方法

Image Reconstruction Based on Improved Backward Optimized Orthogonal Matching Pursuit Algorithm

现有的正交匹配追踪(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,这使其需要通过非常多的线性测量来保证精确重建.为此,文中提出一种改进的后退型最优OMP方法:首先利用最优正交匹配追踪(OOMP)算法在迭代过程中通过最优的正交化性来约束原子的选择,以保证原子的选择在最小化当前冗余误差的意义下最优;然后将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来对前面得到的迭代结果进行后处理,并向后剔除其中多余的原子,从而获得精确重建.模拟信号和真实图像实验结果表明,与OMP算法相比,采用改进算法可以获得精确重建并大大降低对测量数目的要求.

As the existing orthogonal matching pursuit （OMP） algorithms acquire the reconstruction with given number of iterations, i.e. given sparsity level of the image to be reconstructed, many linear measurements are needed to ensure the reconstruction accuracy. In order to reduce the number of linear measurements, an improved backward-optimized OMP algorithm is presented, in which an optimized orthogonal matching pursuit （OOMP） algorithm is adopted to restrict the selection of atoms based on the optimized orthogonality in the iteration process, thus optimizing the selection of atoms with a minimum current residual error. The sparsity level is then taken as the standard of the adaptive iteration number, and a very simple principle of atom selection is proposed to post-process the iteration results, thus backward eliminating the superfluous atoms and acquiring exact reconstruction. Simulated and experimental results indicate that, as compared with the existing OMP algorithms, the proposed algorithm helps to acquire the reconstruction with higher accuracy and fewer measurements.