Although compressed sampling can relieve the pressure of data storage and transmission in the field of mechanical condition monitoring，the reconstruction of compressed data has always been a challenge. Aiming at the problem of fault extraction from compressed rolling bearing signals，a reconstruction method for fault signal based on the feature proxy and convex optimization algorithm is developed. The sparse and convolutional characteristics of localized bearing fault signal are analyzed，and the fault impact pattern is learned. For the compressed bearing signal，the proxy containing the information of impact occurrence time is constructed. An optimization function is established for the proxy，and the sparse coefficient is extracted from the proxy with the Fast Iterative Shrinkage Thresholding Algorithm（FISTA）. Finally，the fault signal is reconstructed by the convolution between the impact pattern and the sparse coefficient. Compared with the direct impact feature extraction from compressed signal using the FIT-SA，the proposed method reduces the computational complexity while without reducing the accuracy of the solution. When compared with the commonly used greedy reconstruction algorithm，the proposed method does not require the prior estimation of signal sparsity，and can get the global optimal solution. The rolling bearing simulation and experimental analysis further verify the effectiveness of the proposed method.