Sparse Reconstruction Based on the ADMM and Lasso-LSQR for Bearings Vibration Signals

In this paper, we introduce a novel method for reconstructing roller bearings vibration signals. As well as the sparse reconstruction algorithm, our approach is based on the Lasso via the alternate direction multiplier method (ADMM) and optimized by least square QR-factorization (LSQR), which takes the priority over the Basis Pursuit and Lasso in iterations and errors. First, we use the discrete cosine transformation to achieve sparse signals, then we compress signals by using the Gaussian random matrix, and, finally, we reconstruct the original signals with the Lasso-LSQR by using the ADMM. According to the results, vibration signals can keep sufficient reconstruction accuracy with high compressive ratio, which validates the effectiveness of the method for vibration signals.