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This paper addresses the problem of interferometric noise reduction in Synthetic Aperture Radar (SAR) interferometry based on sparse and redundant representations over a trained dictionary. The idea is to use a Proximity-based K-SVD (ProK-SVD) algorithm on interferometric data for obtaining a suitable dictionary, in order to extract the phase image content effectively. We implemented this strategy on both simulated as well as real interferometric data for the validation of our approach. For synthetic data, three different training dictionaries have been compared, namely, a dictionary extracted from the data, a dictionary obtained by a uniform random distribution in [ − π , π ] , and a dictionary built from discrete cosine transform. Further, a similar strategy plan has been applied to real interferograms. We used interferometric data of various SAR sensors, including low resolution C-band ERS/ENVISAT, medium L-band ALOS, and high resolution X-band COSMO-SkyMed, all over an area of Mt. Etna, Italy. Both on simulated and real interferometric phase images, the proposed approach shows significant noise reduction within the fringe pattern, without any considerable loss of useful information. [ABSTRACT FROM AUTHOR]