In this paper, we introduce new multiscale AM-FM demodulation algorithms that provide significant improvements in accuracy over previously reported approaches. The improvements are due to the use of new filterbanks based on separable filters supported in just two quadrants. The QEA, robust-QEA and Vakman methods are improved with this new filterbanks. A number of 2-D AM-FM examples are presented, where we observe significant accuracy improvements. For Lena, the mean-square-error for the AM-FM harmonic reconstruction is reduced by 88.31%. Similarly, for a AM-FM synthetic example of sinusoidal phase and Gaussian amplitude, the meansquare-error is reduced by: (i) 70.86% for the reconstruction, (ii) 99.66% for the instantaneous amplitude and (iii) 96.52% for the sinusoidal instantaneous frequency component. © 2007 IEEE.