The paper proposes a new method for performing multi-resolution analysis (MRA) of non-uniform data with jump discontinuities and impulsive noise using robust M-estimator-based local polynomial regression (LPR). The basic idea is to interpolate the smoothed estimate, after performing the robust LPR, on a uniform grid in order to perform the MRA using the ordinary wavelet transform. Simulation results show that the new approach performs better than traditional LS-based LPR in preserving jump discontinuities and suppressing isolated impulses when intersection confident intervals (ICI) bandwidth selection is employed.