基于局部随机化哈达玛矩阵的正交多匹配追踪算法

Orthogonal multi matching pursuit algorithm based on local randomized Hadamard matrix

针对现有测量矩阵的优缺点,采用具有良好相关性、随机独立性及快速计算的局部随机化哈达玛矩阵作为测量矩阵,同时针对标准正交匹配追踪算法在测量过程中受扰或在稀疏信号情况下难以稳定精确重构问题,提出了一种基于局部随机化哈达玛矩阵的正交多匹配追踪算法。该算法利用局部随机化哈达玛矩阵的结构特性,能够快速精确重构原信号。仿真结果表明,测量过程中存在噪声或无噪,无论处理一维信号还是二维图像信号时,该算法性能均超过同类其他贪婪算法和凸优化基匹配法。

According to advantages and drawbacks of existing measurement matrixes, a local randomized Hadamard matrix is adopted, which has high eorrelativity, stochastic independence and fast computation capa- bility. Meanwhile, according to the question which is hard to reconstruct stably original signals for the standard orthogonal matching pursuit （OMP） algorithm when the samples are compressible signals or are contaminated with noises, a novel orthogonal multimatching pursuit algorithm based on local randomized Hadamard matrix is proposed. The proposed algorithm can precisely reconstruct signals by using the special structural features of the local randomized Hadamard matrix. The simulation results of one dimensional signals and real image show that the proposed algorithm is superior to other greedy algorithms and convex basis pursuit（BP） method no mat- ter whether the samples are contaminated with noise or not.