Phase unwrapping arises as a key step in several imaging technologies, from which we emphasize remote sensing applications like terrain analysis and generation, topographic mapping, interferometric synthetic aperture radar (ISAR). Due to various decorrelation factors, there is much noise in phase images. Phase noise degrades the visual quality of images and interferograms, increases the errors of results derived from the ISAR interferogram, and obstruct phase unwrapping. Hilbert transform (HT) as a phase unwrapping techniques was recently proposed, and its behavior in presence of noise is unknown. In this paper, one-dimensional (1-D) HT phase unwrapping algorithm is proposed to detect and eliminate phase discontinuities in N-dimensional (ND) noisy phase arrays. The behavior of this method in presence of different noise levels is studied and compared with the other approach of phase jump detection. The phase noise filtration problem and its effect on proposed algorithm behavior are considered. Tests of method presented illustrate the validity and effectiveness of proposed algorithm for difficult problems with noisy and discontinuous original phases.