An improved reconstruction method based on auto-adjustable step size sparsity adaptive matching pursuit and adaptive modular dictionary update for acoustic emission signals of rails

•Wavelet-packet transform is used to reveal the differences between signals.•Multiscale-modular dictionary is trained parallel to increase the training speed.•Kurtosis is used to improve the accuracy of the sparsity adaptive matching pursuit.•The dictionary’s adaptability is enhanced by the adaptive modular dictionary update.•The proposed method is verified through the tensile test based on intact rail.