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This paper develops mathematical techniques and makes use of interferometric synthetic aperture radar (InSAR) for improving the quality of digital elevation models derived from SAR images and providing accurate estimations of atmospheric path and absolute phase delays and water vapor content estimation. The problem of solving parameters such as atmospheric path delay, height, and unwrapping errors is to be described in a mathematical form that uses QR factorization techniques for solving rank-deficient systems. A new approach for the solution of rank-deficient systems with few independent equations is proposed. In the new approach, the bounds are considered known and provided by the eigenvalues. New eigenvalues are added inside the bounds. During the implementation, attention is given not to exceed the bounds of the reorganized matrix. This approach is the first time that is used for phase parameterization in terms of height, tropospheric delay, and phase unwrapping errors. Expanding the approach was also studied for absolute phase delay and water vapor content estimation. The investigation and the implementation of the approach make use of ENVISAT images. The validation of results was implemented through GPS and meteorological measurements.