Atmospheric delay is one of the major sources of error in repeat pass interferometry. We propose a new approach for correcting the topography-correlated components of this artifact. To this aim we use multiresolution wavelet analysis to identify the components of the unwrapped interferogram that correlate with topography. By using a forward wavelet transform we break down the digital elevation model and the unwrapped interferogram into their building blocks based on their frequency properties. We apply a cross-correlation analysis to identify correlated coefficients that represent the effect of the atmospheric delay. Thus, the correction to the unwrapped interferogram is obtained by down-weighting the correlated coefficients during inverse wavelet transform. We test this approach on real and synthetic data sets that are generated over the San Francisco Bay Area. We find that even in the presence of tectonic signals, this method is able to reduce the correlated component of the atmospheric delay by up to 75% and improves the signal in areas of high relief. The remaining part is most likely due to 3D heterogeneities of the atmosphere and can be reduced by integrating temporal information or using complementary observations or models of atmospheric delay.