This paper addresses the problem of interferometric phase noise reduction in synthetic aperture radar interferometry. A new phase noise model in the complex domain is introduced and validated by using both simulated and real interferograms. This noise model is also derived in the complex wavelet domain, where a novel noise reduction algorithm, which is not based on a windowing process and without the necessity of phase unwrapping, is addressed. The use of the wavelet transform allows to maintain the spatial resolution in the filtered phase image and prevents to filter low coherence areas. By using both, simulated as well as real interferometric phase images, the performance of this algorithm, in terms of noise reduction, spatial resolution maintenance, and computational efficiency, is reported and compared with other conventional filtering approaches.