Robust phase unwrapping and its applications in radar signal processing and imaging.

摘要

Phase unwrapping is the reconstruction of a phase function on a grid given the value modulo 2pi of the function on the grid. This is an important process in signal and image processing. An important technique in phase unwrapping is to use the Chinese remainder theorem (CRT) to determine a true frequency from its multiple wrapped versions (remainders). It is well known that the CRT has tremendous applications in many fields, but it is not robust in the sense that a small error in any remainders may cause a large error in the reconstruction result, which is well-known not robust. This is perhaps why CRT has applications in cryptography but not desired in some other applications, such as frequency estimation from undersampled waveforms with its applications, for example, phase unwrapping in radar signal processing and sensor networks. Recently, a robust phase unwrapping algorithm has been proposed, that has already found applications in (multi-baseline, multifrequency, multi-speed, multi-stepped frequency, multi-pulse repetition frequency) SAR imaging for moving targets. Regarding the computational complexity of this robust phase unwrapping algorithm, an efficient implementation is developed to reduce the two dimensional searching of its original into a one dimensional searching, and therefore reduces the complexity significantly.;What is more, motivated from the robust phase unwrapping algorithm, a general form of robust CRT is proposed, i.e., robust reconstruction of general large integers from their remainders with errors. This case often occurs in practical applications, that is the reason why a robust solution is urgently needed. In terms of reconstruction of large integers from remainders, it is not restricted to co-prime moduli, and this unique reconstruction is possible if and only if the large integers are less than the least common multiple (lcm) of all the moduli. Note that this proposed algorithm is for a general real number, for those with zero fractional errors, the algorithm then leads to a fast robust CRT.;Further, some applications based on this robust algorithm are developed, including a robust Doppler ambiguity resolution using multiple paired pulse repetition frequencies (PRF). This new algorithm is based on this robust phase unwrapping algorithm and the Ferrari-B´erenguer-Alengrin (FBA) method using multiple pulse repetition frequencies (PRF). Our simulation results show that the newly proposed algorithm significantly outperforms the FBA method and is also better than the robust phase unwrapping algorithm.;Moreover, another important topic and application, location and imaging of elevated moving targets using multiple frequency velocity synthetic aperture radar (SAR), is well investigated and proposed. In this dissertation, we propose an antenna array approach with cross-track interferometry, in which multiple wavelength signals are transmitted. It is shown that our proposed multiple-frequency interferometric velocity SAR (MFIn-VSAR) by applying our proposed robust phase unwrapping algorithm can locate both slowly and fast moving elevated targets correctly. An integrated MFIn-VSAR algorithm for moving target imaging is also presented.