对含噪微机械系统（MEMS）陀螺信号进行小波分解重构时，真实信号对应的小波系数很难选取，故本文提出一种分层自适应匹配追踪算法(LAMP)来解决上述问题。建立了含噪MEMS陀螺信号中信号小波系数稀疏提取架构，将信号小波系数提取问题转化为含噪信号中信号小波系数稀疏性的恢复问题。比较已有稀疏重构算法，采用一种新的LAMP算法，在各种可能的小波系数组合中挑选出分解系数最为稀疏的一组，以此消除信号中的噪声小波系数，进而重构MEMS陀螺信号。实验表明：提出的LAMP算法的稀疏重构效果优于其他迭代贪婪重构算法；基于LAMP的信号稀疏小波重构方法，可以有效去除MEMS陀螺信号的大量噪声；去噪前后，纯MEMS陀螺数据解算的方位角平均累积误差由10.060 2 （°）/h减小到5.034 6 （°）/h，优于传统小波阈值重构法平均累积误差8.596 8 (°)/h， 显示了较好的应用效果。

When noisy signals from a Micro-electromechanical System(MEMS) gyro are reconstructed by wavelet decomposes, it is difficult to choose the wavelet coefficients corresponding to the real signals. Therefore, a kind of Layerwise and Adaptive Matching Pursuit-based(LAMP-based)algorithm was proposed to solve the problem mentioned above. A sparse extraction construction of wavelet coefficients from the real MEMS gyro signal was established by recovering the sparsity of the wavelet coefficients of the noisy gyro signal. Then, the new LAMP algorithm was designed to pick out the most sparse wavelet coefficients among all wavelet coefficients of the noisy MEMS gyro signal, and the chosen wavelet coefficients were utilized to reconstruct the real MEMS gyro signal. Substantial experiment results indicate that the proposed LAMP algorithm is superior to other iterative greedy reconstruction algorithms. It effectively removes substantial MEMS gyro noise, and corresponding azimuth average error reduces from 10.060 2 （°）/h (before LAMP reconstruction) to 5.034 6 （°）/h (after LAMP reconstruction), which shows its denoising performance to be better than that of the traditional wavelet threshold reconstruction method with an azimuth average error of 8.596 8 (°)/h(after wavelet threshold reconstruction). It concludes that the proposed LAMP-based signal reconstruction method for MEMS gyro has good application prospect.