Weighted denoising for phase unwrapping
Weighted denoising for phase unwrapping
复制标题
用于相位展开的加权去噪
DOI：
10.1117/12.2039390
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
Shusuke Nishiyama
中科院分区：
文献类型：
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作者：
Satoshi Tomioka;Shusuke Nishiyama
为了测量随时间快速变化的物体的光程，傅里叶变换方法是合适的，因为它只需要单个干涉图。在测量这种快速现象时，由于相机曝光时间短，相机记录干涉图的热噪声会导致显着误差，并且信号变得很弱。当噪声水平高时，为了获得光学距离分布，在相位展开之前应增加对包裹相位的去噪处理。热噪声具有均匀的空间分布;然而，信号取决于入射到干涉仪的波的轮廓。这意味着信噪比具有空间分布。本文提出的去噪方法，可以考虑的数据，取决于信号强度分布的权重。为了确定去噪阶段，检查了两个成本函数。一种是复值代价函数，它能保证迭代法收敛，得到稳定点，但没有证明在稳定点处真实的部分和虚部分都最小。另一种是实值代价函数，它不能保证收敛，但它使代价函数在平稳点处最小化。数值仿真验证了加权去噪的有效性和代价函数的适用性。
In order to measure the optical distance of the object that changes rapidly over time, Fourier transform method is appropriate because it requires only a single interferogram. In the measurements of such fast phenomena, the thermal noise by the camera to record the interferogram results in a significant error and the signal becomes weak owing to the short exposure time of the camera. When the noise level is high, a process to denoise wrapped phase should be added before phase unwrapping in order to obtain an optical distance distribution. The thermal noise has a uniform spatial distribution; however, the signal depends on a profile of the incident wave to the interferometer. This means that the signal to noise ratio has a spatial distribution. This paper proposes the denoising method that can take account of the weight of the data that depends on the signal intensity distribution. In order to determine the denoised phase, two cost functions are examined. One is a complex-valued cost function that can ensure convergence of iterative method to obtain the stationary point; however, it is not proved that both the real part and the imaginary part are minimized at the stationary point. The other is a real-valued cost function that cannot ensure the convergence but it minimizes the cost function at the stationary point. The numerical simulation demonstrates the validity of the weighted denoising and the applicability of the cost functions.