The asymptotic properties of polynomial phase estimation by least squares phase unwrapping

Phase-shifting interferometry on structured light projection is widely used in 3-D surface measurement. An investigation shows that least-squares fitting can significantly decrease random error by incorporating data from the intermediate phase values, but it cannot completely eliminate nonlinear error. This paper proposes an error-reduction method based on double three-step phase-shifting algorithm and least-squares fitting, and applies it on the temporal phase unwrapping algorithm using three-frequency heterodyne principle. Theoretical analyses and experiment results show that this method can greatly save data acquisition time and improve the precision.

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Functional Linear Regression

10.1093/oxfordhb/9780199568444.013.2 ◽

2018 ◽

Author(s):

Hervé Cardot ◽

Pascal Sarda

Keyword(s):

Linear Regression ◽

Least Squares ◽

Linear Models ◽

Estimation Error ◽

Asymptotic Properties ◽

Principal Component Regression ◽

Principal Component ◽

Penalized Least Squares ◽

Open Problems ◽

Functional Linear Regression

This article presents a selected bibliography on functional linear regression (FLR) and highlights the key contributions from both applied and theoretical points of view. It first defines FLR in the case of a scalar response and shows how its modelization can also be extended to the case of a functional response. It then considers two kinds of estimation procedures for this slope parameter: projection-based estimators in which regularization is performed through dimension reduction, such as functional principal component regression, and penalized least squares estimators that take into account a penalized least squares minimization problem. The article proceeds by discussing the main asymptotic properties separating results on mean square prediction error and results on L2 estimation error. It also describes some related models, including generalized functional linear models and FLR on quantiles, and concludes with a complementary bibliography and some open problems.

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Comparison of path-following and least-squares phase unwrapping algorithms

IGARSS'97. 1997 IEEE International Geoscience and Remote Sensing Symposium Proceedings. Remote Sensing - A Scientific Vision for Sustainable Development ◽

10.1109/igarss.1997.615283 ◽

2002 ◽

Cited By ~ 6

Author(s):

M.D. Pritt

Keyword(s):

Least Squares ◽

Path Following ◽

Phase Unwrapping

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A Robust Discontinuous Phase Unwrapping Based on Least-Squares Orientation Estimator

Electronics ◽

10.3390/electronics10222871 ◽

2021 ◽

Vol 10 (22) ◽

pp. 2871

Author(s):

Gaoxu Deng ◽

Shiqian Wu ◽

Shiyang Zhou ◽

Bin Chen ◽

Yucheng Liao

Keyword(s):

Least Squares ◽

Weighted Least Squares ◽

Bilateral Filter ◽

Phase Unwrapping ◽

Noise Variance ◽

Post Processing ◽

Quadratic Error ◽

Error Norm ◽

Discontinuous Phase ◽

Simulation Results

Weighted least-squares (WLS) phase unwrapping is widely used in optical engineering. However, this technique still has issues in coping with discontinuity as well as noise. In this paper, a new WLS phase unwrapping algorithm based on the least-squares orientation estimator (LSOE) is proposed to improve phase unwrapping robustness. Specifically, the proposed LSOE employs a quadratic error norm to constrain the distance between gradients and orientation vectors. The estimated orientation is then used to indicate the wrapped phase quality, which is in terms of a weight mask. The weight mask is calculated by post-processing, including a bilateral filter, STDS, and numerical relabeling. Simulation results show that the proposed method can work in a scenario in which the noise variance is 1.5. Comparisons with the four WLS phase unwrapping methods indicate that the proposed method provides the best accuracy in terms of segmentation mean error under the noisy patterns.

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