The orthogonal matching pursuit (OMP) is one of the mainstream algorithms for sparse data reconstruction or approximation. It acts as a driving force for the development of several other greedy methods for sparse data reconstruction, and it also plays a vital role in the development of compressed sensing theory for sparse signal and image reconstruction. In this paper, we propose the so-called dynamic orthogonal matching pursuit (DOMP) and enhanced dynamic orthogonal matching pursuit (EDOMP) algorithms which are more efficient than OMP for sparse data reconstruction from a numerical point of view. We carry out a rigorous analysis to establish the reconstruction error bound for DOMP under the restricted isometry property of the measurement matrix. The main result claims that the reconstruction error via DOMP can be controlled and measured in terms of the number of iterations, sparsity level of data, and the noise level of measurements. Moveover, the finite convergence of DOMP for a class of large-scale compressed sensing problems is also shown.

翻译：正交匹配追踪(OMP)是稀疏数据重建或逼近的主流算法之一。它不仅推动了多种稀疏数据重建贪婪方法的发展，且在稀疏信号与图像重建的压缩感知理论构建中扮演关键角色。本文提出动态正交匹配追踪(DOMP)及增强型动态正交匹配追踪(EDOMP)算法，从数值计算角度而言，它们比OMP更高效。我们基于测量矩阵的约束等距性质，对DOMP的重建误差界进行了严格分析。主要结论表明：DOMP的重建误差可通过迭代次数、数据稀疏度及测量噪声水平等参数进行控制与度量。此外，还证明了DOMP在一类大规模压缩感知问题中的有限收敛性。