Blind deconvolution is a method for enhancing the fault feature of rolling element bearings. Based on different maximization criteria, including kurtosis, correlated kurtosis, D-norm, multi-D-norm, and cyclostationarity indicator, different blind deconvolution algorithms have been proposed as powerful tools for fault feature extraction. However, kurtosis and D-norm are susceptible to extreme values, while the other three criteria strongly rely on prior knowledge of the fault period. To overcome the shortcomings of the existing criteria, this study proposes a new criterion called impulse-norm. It is a time-domain parameter defined as the ratio of the average amplitude of the first several maximum energy points to the energy of the entire signal. As opposed to kurtosis and D-norm, the impulse-norm is not affected by strong random impulses. Unlike correlation kurtosis, multi-D-norm and cyclostationarity indicator, it is also independent from the fault period. Based on impulse-norm, we also propose a new deconvolution algorithm called particle swarm optimization-based maximum impulse-norm deconvolution. This blind deconvolution algorithm employs generalized sphere coordinate transformation and adopts the PSO algorithm to optimally solve the filter coefficients by maximizing the impulse-norm of the signal being filtered. The proposed method was validated using simulated signals and high-speed train axle-box bearing experimental signals. The simulation and experimental results indicated that the proposed PSO-MIND method can effectively identify the weak impulse fault feature of rolling element bearings.