Phase Unwrapping Algorithm Based On Least Squares

The phase contains a lot of useful information,which is widely used in speckle interferometry,magnetic resonance imaging,interferometric synthetic aperture radar,and fringe projection.However,the phase extracted in these measurement techniques is usually not the real continuous phase,but a wrapped phase located in a certain main value interval obtained by operations such as arctangent.Therefore,phase unwrapping,that is,recovering the true phase from the acquired wrapped phase,is of great significance in many phase measurement techniques.Since the 1960 s,many scholars at home and abroad have carried out a lot of research and proposed a variety of different phase unwrapping algorithms.These algorithms generally fall into two categories: path integration based and minimum norm based phase unwrapping.The unwrapping algorithm based on path integration is to select a suitable integration path through a certain strategy,and integrate according to the selected path to complete the phase unwrapping.The minimum norm based unwrapping algorithm solves the real phase by transforming the phase unwrapping problem into an objective function optimization problem.In practical applications,the wrapped phase map obtained by the arctangent operation is often affected by factors such as under-sampling,noise or discontinuity,which increases the difficulty of phase unwrapping,and as a result,there is still no algorithm that can solve the problem perfectly.For the phase unwrapping problem,different algorithms still have a lot of space for improvement.This paper studies the phase unwrapping algorithm based on least squares.The main work of the paper is as follows:(1)The research background and current status of phase unwrapping at home and abroad are briefly introduced,and the principles,advantages and disadvantages of commonly used algorithms in phase unwrapping based on path integral and minimum norm are introduced.(2)Existing algorithms generally have low unwrapping accuracy for high-noise wrapped phase maps.Many existing methods based on pre-filtering are parametric and interactive,with high computational complexity.Therefore,a phase unwrapping algorithm with simultaneous unwrapping and filtering is studied in this paper.The algorithm relies on the solution of the four-way least squares discrete cosine transform of phase unwrapping.The noise in the image is reduced by adding a threshold operation to the coefficients of expanded discrete cosine transform,and then the unwrapping phase is obtained by the inverse discrete cosine transform,so as to realize the simultaneous unwrapping and filtering.In order to further suppresses the influence of noise on the unwrapping results and effectively improve the unwrapping accuracy,an iterative compensation operation for unwrapping error is added.The effectiveness and robustness of the proposed algorithm are verified by comparison experiments with the commonly used unwrapping algorithms.(3)When the phase gradient changes greatly,that is,the phase difference between adjacent pixels does not meet the continuity requirement in the numerical method,the propagation of the unwrapping error in the discontinuous region makes the unwrapping more difficult.Aiming at the unwrapping problem of discontinuous wrapped phase,this paper studies a phase unwrapping algorithm based on global variation and adaptive weights.Different weight parameters are used at the phase continuity and discontinuity respectively,and the phase discontinuity is limited to the region with very low weight value,so that the place with large phase gradient can also meet the continuity requirement of the numerical method,and the accuracy of unwrapping is proved.The comparison experiments with the commonly used unwrapping algorithms verify the effectiveness of the presented algorithm.