Modified variational image decomposition algorithm aided by the Hilbert transform as an alternative to 2D Hilbert-Huang transform for fringe pattern phase retrieval

The process of information recovering from fringe pattern can be divided into two main parts: filtration (fringe pattern background and noise removal) and phase (or amplitude) demodulation. In recent years the 2D Hilbert spiral transform (HST) has become one of the most popular phase demodulation techniques. Together with empirical mode decomposition used for fringe pattern preprocessing forms a strong fringe pattern analysis algorithm called 2D HilbertHuang transform (HHT). Variational image decomposition was recently adapted for fringe pattern filtration. In combination with the 2D Hilbert spiral transform and after some modifications it might become an excellent tool for fringe pattern analysis purpose and can compete with well-developed HHT. Proposed modification is the first attempt to automate the variational image decomposition in terms of fringe pattern filtration. Received results show that VID-HST can compete with HHT and may become an excellent alternative for fringe pattern evaluation. Another fact encouraging the development of VID is a wide range of applications that have been proposed up to now, i.e., image denoising, fringe pattern filtration and phase filtration.

[1]  Linlin Wang,et al.  Phase retrieval from single frame projection fringe pattern with variational image decomposition , 2014 .

[2]  Krzysztof Patorski,et al.  Hilbert-Huang single-shot spatially multiplexed interferometric microscopy. , 2018, Optics letters.

[3]  Wang-Q Lim,et al.  The Discrete Shearlet Transform: A New Directional Transform and Compactly Supported Shearlet Frames , 2010, IEEE Transactions on Image Processing.

[4]  Krzysztof Patorski,et al.  Quantitative phase imaging by single-shot Hilbert-Huang phase microscopy. , 2016, Optics letters.

[5]  M. Takeda,et al.  Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry , 1982 .

[6]  A. Bovik,et al.  A universal image quality index , 2002, IEEE Signal Processing Letters.

[7]  Marc Lebrun,et al.  An Analysis and Implementation of the BM3D Image Denoising Method , 2012, Image Process. Line.

[8]  Chen Tang,et al.  A 3D shape retrieval method for orthogonal fringe projection based on a combination of variational image decomposition and variational mode decomposition , 2016 .

[9]  L. Rudin,et al.  Nonlinear total variation based noise removal algorithms , 1992 .

[10]  Yves Meyer,et al.  Oscillating Patterns in Image Processing and Nonlinear Evolution Equations: The Fifteenth Dean Jacqueline B. Lewis Memorial Lectures , 2001 .

[11]  Yonggang Su,et al.  Variational image decomposition for estimation of fringe orientation and density from electronic speckle pattern interferometry fringe patterns with greatly variable density , 2016 .

[12]  Zeev Zalevsky,et al.  Superresolved spatially multiplexed interferometric microscopy. , 2017, Optics letters.

[13]  Krzysztof Patorski,et al.  Adaptive enhancement of optical fringe patterns by selective reconstruction using FABEMD algorithm and Hilbert spiral transform. , 2012, Optics express.

[14]  Zeev Zalevsky,et al.  Spatially-multiplexed interferometric microscopy (SMIM): converting a standard microscope into a holographic one. , 2014, Optics express.

[15]  Alessandro Foi,et al.  Image Denoising by Sparse 3-D Transform-Domain Collaborative Filtering , 2007, IEEE Transactions on Image Processing.

[16]  Chunmin Zhang,et al.  Empirical mode decomposition based background removal and de-noising in polarization interference imaging spectrometer (vol 21, pg 2592, 2013) , 2013 .

[17]  Jean Claude Nunes,et al.  Texture analysis based on local analysis of the Bidimensional Empirical Mode Decomposition , 2005, Machine Vision and Applications.

[18]  Maciej Trusiak,et al.  Advanced processing of optical fringe patterns by automated selective reconstruction and enhanced fast empirical mode decomposition , 2014 .

[19]  N. Huang,et al.  The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis , 1998, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[20]  Jesmin F. Khan,et al.  Fast and Adaptive Bidimensional Empirical Mode Decomposition Using Order-Statistics Filter Based Envelope Estimation , 2008, EURASIP J. Adv. Signal Process..

[21]  Gitta Kutyniok,et al.  From Wavelets to Shearlets and back again , 2007 .

[22]  Alejandro Federico,et al.  Evaluation of the 1D empirical mode decomposition method to smooth digital speckle pattern interferometry fringes , 2007 .

[23]  Manuel Servin,et al.  Fringe Pattern Analysis for Optical Metrology: Theory, Algorithms, and Applications , 2014 .

[24]  ANTONIN CHAMBOLLE,et al.  An Algorithm for Total Variation Minimization and Applications , 2004, Journal of Mathematical Imaging and Vision.

[25]  Antonin Chambolle,et al.  Dual Norms and Image Decomposition Models , 2005, International Journal of Computer Vision.

[26]  Maciej Trusiak,et al.  Single-frame fringe pattern analysis using modified variational image decomposition aided by the Hilbert transform for fast full-field quantitative phase imaging , 2018, Photonics Europe.

[27]  M. A. Oldfield,et al.  Natural demodulation of two-dimensional fringe patterns. I. General background of the spiral phase quadrature transform. , 2001, Journal of the Optical Society of America. A, Optics, image science, and vision.

[28]  Maciej Trusiak,et al.  Single shot fringe pattern phase demodulation using Hilbert-Huang transform aided by the principal component analysis. , 2016, Optics express.

[29]  Xinjun Zhu,et al.  Variational image decomposition for automatic background and noise removal of fringe patterns. , 2013, Optics letters.

[30]  Stanley Osher,et al.  Modeling Textures with Total Variation Minimization and Oscillating Patterns in Image Processing , 2003, J. Sci. Comput..

[31]  Zeev Zalevsky,et al.  Spatially multiplexed interferometric microscopy with partially coherent illumination , 2016, Journal of biomedical optics.

[32]  Catalina Sbert,et al.  Chambolle's Projection Algorithm for Total Variation Denoising , 2013, Image Process. Line.

[33]  Alejandro Federico,et al.  Noise reduction in digital speckle pattern interferometry using bidimensional empirical mode decomposition. , 2008, Applied optics.