一种基于最小一乘法的相位展开评估方法

An assessment of phase unwrapping based on least absolute deviation

相位展开是基于相位的三维光栅投影测量的关键环节。为了评估相位展开算法的优劣,需要用全面系统的方法对算法进行综合评价。基于范数理论,以最小一乘法为基础,以DCT(离散余弦变换法)为代表进行讨论,以一乘不连续点数定量描述相位展开的稳定性和细节还原性,以弥补仅用均方根误差和残差点数等方法的评估盲区,从而更全面地评估相位展开算法。给出了该评估方法的基本原理及仿真,对仿真结果进行评价,对相位展开算法的评估方法研究起到抛砖引玉的作用。

Phase unwrapping is a key link in phase based three-dimensional grating projecting measurement. In order to assess the phase unwrapping methods, a comprehensive and systematic approach is needed. In this paper,DCT（ discrete cosine transform）,as the representation of the least square method,is evaluated based on the least absolute deviation and norm theory. The robustness of the phase unwrapping algorithm and detail recovery are quantitively appraised based on the number of uncontinuous points in the least absolute deviation method. This evaluation method can cover the assessment blind areas in those that are only based on the square root error and residual points,and thus evaluate phase unwrapping in a more comprehensive way. The basic principle and simulation are introduced and the simulation results are evaluated,which tries to throw away a brick to get a gem in the appraisal research of phase unwrapping.