At early stage of bearing fault,the feature components of the original vibration signal are easy to be submerged in strong background noise and thus are hard to be detected． With sparse representation theory, a novel method for transient sparse representation under wavelet basis is proposed. Sparse representation model is firstly constructed, correlation filtering is applied to obtain optimal wavelet atom, thus the optimal redundant wavelet basis, which can best match the transient features of the signal is realized. A designed strictly convex quadratic function is incorporated into Majorization Minimization (MM) algorithm to solve the objective function. With the proposed method, transients hidden in the noisy signal can be converted into sparse coefficients, thus the transients can be detected sparsely. Both the simulation and a real application of rolling bearings with weak fault demonstrate that the weak transients can be effectively obtained through the proposed method.