To get a better de-noising effect

a novel noise reduction method combining the sparse decomposition with lifting wavelet transform is proposed. Firstly

the error model is established for the MEMS gyroscope output signal with noise

and wavelet coefficient of signals with noise can be obtained by lifting wavelet transform. Then the sparsity of the coefficient is recovered according to sparse decomposition theory. Finally

signals are reconstructed by lifting wavelet inverse transform

i.e. the de-noised signal is thus obtained. In addition

since the gradient projection algorithm is global optimal algorithm with high computational efficiency

the theory of gradient projection is used in the restoration of sparse signal. Specifically

a sparse decomposition based on gradient projection is designed to simplify the algorithm complexity and improve the stability of the algorithm. To verify the performance of the proposed algorithm

the static experiment and dynamic car test on MEMS gyroscope are implemented. The results show that the denoising performance of the new method is better than that of wavelet filter either under the static or dynamic condition

especially under the latter condition. Meanwhile

the CPU time of gradient projection is less than orthogonal matching pursuit (OMP) and basis pursuit (BP).