Traditional impulse quantization index in bearing fault diagnosis is limited in performance which can't correctly indicate the bearing fault bands under the mask of strong background noise. To solve this problem, RNSE (reweighted negentropy of the squared envelope) and RNSES (reweighted negentropy of the square envelope spectrum) were proposed which were sensitive to faulty periodic impulses and robust to random impulses without prior knowledge of the fault periodicity. Furthermore, the Rinfogram (reweighted Infogram) was proposed based on RNSE and RNSES to extract the fault features from bearing vibration signals. Validations on bearing fault simulation signals and high-speed train traction motor bearing bench test signals showed that Rinfogram was robust to random pulses and could successfully identify the fault frequency bands under strong noise interference. There is evidence that Rinfogram is better than Kurtogram based on spectral kurtosis and traditional Infogram in fault feature extraction effect, which improves the accuracy of bearing fault diagnosis.