J. Wu and C. Tang, “PDE-based random-valued impulse noise removal based on new class of controlling functions,” IEEE Trans. Image Process. 20, 2428–2438 (2011).

[CrossRef]

L. Cheng, C. Tang, S. Yan, X. Chen, L. Wang, and B. Wang, “New fourth-order partial differential equations for filtering in electronic speckle pattern interferometry fringes,” Opt. Commun. 284, 5549–5555 (2011).

[CrossRef]

C. Tang, L. Han, H. Ren, T. Gao, Z. Wang, and K. Tang, “The oriented-couple partial differential equations for filtering in wrapped phase patterns,” Opt. Express 17, 5606–5617 (2009).

[CrossRef]

H. Wang, Q. Kemao, W. Gao, F. Lin, and H. S. Seah, “Fringe pattern denoising using coherence enhancing diffusion,” Opt. Lett. 34, 1141–1143 (2009).

[CrossRef]

C. Tang, W. Lu, S. Chen, Z. Zhang, B. Li, W. Wang, and Lin Han, “Denoising by coupled partial differential equations and extracting phase by backpropagation neural networks for electronic speckle pattern interferometry,” Appl. Opt. 46, 7475–7484 (2007).

[CrossRef]

H. M. Salinas and D. C. Fernández, “Comparison of PDE-based nonlinear diffusion approaches for image enhancement and denoising in optical coherence tomography,” IEEE Trans. Med. Imaging 26, 761–771 (2007).

[CrossRef]

T. I. Voronyak, A. B. Kmet’, and O. V. Lychak, “Single-step phase-shifting speckle interferometry,” Mater. Sci. 43, 554–567 (2007).

[CrossRef]

W. Lv, C. Tang, and W. Wang, “Noise reduction in electronic speckle pattern interferometry fringes by fourth-order partial differential equations,” Proc. SPIE 6279, (2007).

[CrossRef]

C. Tang, F. Zhang, H. Yan, and Z. Chen, “Denoising in electronic speckle pattern interferometry fringes by the filtering method based on partial differential equations,” Opt. Commun. 260, 91–96 (2006).

[CrossRef]

C. Tang, F. Zhang, and Z. Chen, “Contrast enhancement for electronic speckle pattern interferometry fringes by the differential equation enhancement method,” Appl. Opt. 45, 2287–2294 (2006).

[CrossRef]

S. K. Weeratunga and C. Kamath, “A comparison of PDE based non-linear anisotropic diffusion techniques for image denoising,” Proc. SPIE 5014, 151493 (2003).

[CrossRef]

M. Lysaker, A. Lundervold, and X.-C. Tai, “Noise removal using fourth-order partial differential equation with applications to medical magnetic resonance images in space and time,” IEEE Trans. Image Process 12, 1579–1590(2003).

[CrossRef]

Y. Chen, C. A. Z. Barcelos, and B. A. Mairz, “Smoothing and edge detection by time-varying coupled nonlinear diffusion equations,” Comput. Vis. Image Understand. 82, 85–100 (2001).

[CrossRef]

X. Su and W. Chen, “Fourier transform profilometry: a review,” Opt. Lasers Eng. 35, 263–284 (2001).

[CrossRef]

Y. You and M. Kaveh, “Fourth-order partial differential equations for noise removal,” IEEE Trans. Image Process. 9, 1723–1730 (2000).

[CrossRef]

H. A. Aebischery and S. Waldner, “A simple and effective method for filtering speckle-interferometric phase fringe patterns,” Opt. Commun. 162, 205–210 (1999).

[CrossRef]

G. Sapiro and D. L. Ringach, “Anisotropic diffusion of multivalued images with applications to color filtering,” IEEE Trans. Image Process 5, 1582–1586 (1996).

[CrossRef]

L. Alvarez, P.-L. Lions, and J.-M. Morel, “Image selective smoothing and edge detection by nonlinear diffusion,” SIAM J. Numer. Anal. 29, 845–866 (1992).

[CrossRef]

L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Physica 60, 259–268 (1992).

[CrossRef]

F. Catté, P.-L. Lions, J.-M. Morel, and T. Coll, “Image selective smoothing and edge detection by nonlinear diffusion,” SIAM J. Numer. Anal. 29, 182–193 (1992).

[CrossRef]

K. H. Womack, “Interferometric phase measurement using spatial synchronous detection,” Opt. Eng. 23, 391–395 (1984).

H. A. Aebischery and S. Waldner, “A simple and effective method for filtering speckle-interferometric phase fringe patterns,” Opt. Commun. 162, 205–210 (1999).

[CrossRef]

L. Alvarez, P.-L. Lions, and J.-M. Morel, “Image selective smoothing and edge detection by nonlinear diffusion,” SIAM J. Numer. Anal. 29, 845–866 (1992).

[CrossRef]

M. Aslan, “Toward the development of high-speed microscopic ESPI system for monitoring laser heating/drilling of alumina Al2O3 substrates,” Ph.D. dissertation (Pennsylvania State University, 2000).

Y. Chen, C. A. Z. Barcelos, and B. A. Mairz, “Smoothing and edge detection by time-varying coupled nonlinear diffusion equations,” Comput. Vis. Image Understand. 82, 85–100 (2001).

[CrossRef]

F. Catté, P.-L. Lions, J.-M. Morel, and T. Coll, “Image selective smoothing and edge detection by nonlinear diffusion,” SIAM J. Numer. Anal. 29, 182–193 (1992).

[CrossRef]

X. Su and W. Chen, “Fourier transform profilometry: a review,” Opt. Lasers Eng. 35, 263–284 (2001).

[CrossRef]

L. Cheng, C. Tang, S. Yan, X. Chen, L. Wang, and B. Wang, “New fourth-order partial differential equations for filtering in electronic speckle pattern interferometry fringes,” Opt. Commun. 284, 5549–5555 (2011).

[CrossRef]

Y. Chen, C. A. Z. Barcelos, and B. A. Mairz, “Smoothing and edge detection by time-varying coupled nonlinear diffusion equations,” Comput. Vis. Image Understand. 82, 85–100 (2001).

[CrossRef]

C. Tang, F. Zhang, H. Yan, and Z. Chen, “Denoising in electronic speckle pattern interferometry fringes by the filtering method based on partial differential equations,” Opt. Commun. 260, 91–96 (2006).

[CrossRef]

C. Tang, F. Zhang, and Z. Chen, “Contrast enhancement for electronic speckle pattern interferometry fringes by the differential equation enhancement method,” Appl. Opt. 45, 2287–2294 (2006).

[CrossRef]

L. Cheng, C. Tang, S. Yan, X. Chen, L. Wang, and B. Wang, “New fourth-order partial differential equations for filtering in electronic speckle pattern interferometry fringes,” Opt. Commun. 284, 5549–5555 (2011).

[CrossRef]

F. Catté, P.-L. Lions, J.-M. Morel, and T. Coll, “Image selective smoothing and edge detection by nonlinear diffusion,” SIAM J. Numer. Anal. 29, 182–193 (1992).

[CrossRef]

L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Physica 60, 259–268 (1992).

[CrossRef]

H. M. Salinas and D. C. Fernández, “Comparison of PDE-based nonlinear diffusion approaches for image enhancement and denoising in optical coherence tomography,” IEEE Trans. Med. Imaging 26, 761–771 (2007).

[CrossRef]

C. Tang, L. Han, H. Ren, T. Gao, Z. Wang, and K. Tang, “The oriented-couple partial differential equations for filtering in wrapped phase patterns,” Opt. Express 17, 5606–5617 (2009).

[CrossRef]

C. Tang, L. Han, H. Ren, D. Zhou, Y. Chang, X. Wang, and X. Cui, “Second-order oriented partial-differential equations for denoising in electronic-speckle-pattern interferometry fringes,” Opt. Lett. 33, 2179–2181 (2008).

[CrossRef]

S. K. Weeratunga and C. Kamath, “A comparison of PDE based non-linear anisotropic diffusion techniques for image denoising,” Proc. SPIE 5014, 151493 (2003).

[CrossRef]

Y. You and M. Kaveh, “Fourth-order partial differential equations for noise removal,” IEEE Trans. Image Process. 9, 1723–1730 (2000).

[CrossRef]

T. I. Voronyak, A. B. Kmet’, and O. V. Lychak, “Single-step phase-shifting speckle interferometry,” Mater. Sci. 43, 554–567 (2007).

[CrossRef]

L. Alvarez, P.-L. Lions, and J.-M. Morel, “Image selective smoothing and edge detection by nonlinear diffusion,” SIAM J. Numer. Anal. 29, 845–866 (1992).

[CrossRef]

F. Catté, P.-L. Lions, J.-M. Morel, and T. Coll, “Image selective smoothing and edge detection by nonlinear diffusion,” SIAM J. Numer. Anal. 29, 182–193 (1992).

[CrossRef]

M. Lysaker, A. Lundervold, and X.-C. Tai, “Noise removal using fourth-order partial differential equation with applications to medical magnetic resonance images in space and time,” IEEE Trans. Image Process 12, 1579–1590(2003).

[CrossRef]

W. Lv, C. Tang, and W. Wang, “Noise reduction in electronic speckle pattern interferometry fringes by fourth-order partial differential equations,” Proc. SPIE 6279, (2007).

[CrossRef]

T. I. Voronyak, A. B. Kmet’, and O. V. Lychak, “Single-step phase-shifting speckle interferometry,” Mater. Sci. 43, 554–567 (2007).

[CrossRef]

M. Lysaker, A. Lundervold, and X.-C. Tai, “Noise removal using fourth-order partial differential equation with applications to medical magnetic resonance images in space and time,” IEEE Trans. Image Process 12, 1579–1590(2003).

[CrossRef]

Y. Chen, C. A. Z. Barcelos, and B. A. Mairz, “Smoothing and edge detection by time-varying coupled nonlinear diffusion equations,” Comput. Vis. Image Understand. 82, 85–100 (2001).

[CrossRef]

P. Perona and J. Malik, “Scale-space and edge detection using anisotropic diffusion,” IEEE Trans. Pattern Anal. Machine Intell. 12, 629–639 (1990).

[CrossRef]

L. Alvarez, P.-L. Lions, and J.-M. Morel, “Image selective smoothing and edge detection by nonlinear diffusion,” SIAM J. Numer. Anal. 29, 845–866 (1992).

[CrossRef]

F. Catté, P.-L. Lions, J.-M. Morel, and T. Coll, “Image selective smoothing and edge detection by nonlinear diffusion,” SIAM J. Numer. Anal. 29, 182–193 (1992).

[CrossRef]

L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Physica 60, 259–268 (1992).

[CrossRef]

P. Perona and J. Malik, “Scale-space and edge detection using anisotropic diffusion,” IEEE Trans. Pattern Anal. Machine Intell. 12, 629–639 (1990).

[CrossRef]

C. Tang, L. Han, H. Ren, T. Gao, Z. Wang, and K. Tang, “The oriented-couple partial differential equations for filtering in wrapped phase patterns,” Opt. Express 17, 5606–5617 (2009).

[CrossRef]

C. Tang, L. Han, H. Ren, D. Zhou, Y. Chang, X. Wang, and X. Cui, “Second-order oriented partial-differential equations for denoising in electronic-speckle-pattern interferometry fringes,” Opt. Lett. 33, 2179–2181 (2008).

[CrossRef]

G. Sapiro and D. L. Ringach, “Anisotropic diffusion of multivalued images with applications to color filtering,” IEEE Trans. Image Process 5, 1582–1586 (1996).

[CrossRef]

L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Physica 60, 259–268 (1992).

[CrossRef]

H. M. Salinas and D. C. Fernández, “Comparison of PDE-based nonlinear diffusion approaches for image enhancement and denoising in optical coherence tomography,” IEEE Trans. Med. Imaging 26, 761–771 (2007).

[CrossRef]

G. Sapiro and D. L. Ringach, “Anisotropic diffusion of multivalued images with applications to color filtering,” IEEE Trans. Image Process 5, 1582–1586 (1996).

[CrossRef]

G. Sapiro, Geometric Partial Differential Equations and Image Analysis (Cambridge University, 2001).

X. Su and W. Chen, “Fourier transform profilometry: a review,” Opt. Lasers Eng. 35, 263–284 (2001).

[CrossRef]

M. Lysaker, A. Lundervold, and X.-C. Tai, “Noise removal using fourth-order partial differential equation with applications to medical magnetic resonance images in space and time,” IEEE Trans. Image Process 12, 1579–1590(2003).

[CrossRef]

L. Cheng, C. Tang, S. Yan, X. Chen, L. Wang, and B. Wang, “New fourth-order partial differential equations for filtering in electronic speckle pattern interferometry fringes,” Opt. Commun. 284, 5549–5555 (2011).

[CrossRef]

J. Wu and C. Tang, “PDE-based random-valued impulse noise removal based on new class of controlling functions,” IEEE Trans. Image Process. 20, 2428–2438 (2011).

[CrossRef]

C. Tang, L. Han, H. Ren, T. Gao, Z. Wang, and K. Tang, “The oriented-couple partial differential equations for filtering in wrapped phase patterns,” Opt. Express 17, 5606–5617 (2009).

[CrossRef]

C. Tang, L. Han, H. Ren, D. Zhou, Y. Chang, X. Wang, and X. Cui, “Second-order oriented partial-differential equations for denoising in electronic-speckle-pattern interferometry fringes,” Opt. Lett. 33, 2179–2181 (2008).

[CrossRef]

C. Tang, W. Lu, S. Chen, Z. Zhang, B. Li, W. Wang, and Lin Han, “Denoising by coupled partial differential equations and extracting phase by backpropagation neural networks for electronic speckle pattern interferometry,” Appl. Opt. 46, 7475–7484 (2007).

[CrossRef]

W. Lv, C. Tang, and W. Wang, “Noise reduction in electronic speckle pattern interferometry fringes by fourth-order partial differential equations,” Proc. SPIE 6279, (2007).

[CrossRef]

C. Tang, F. Zhang, H. Yan, and Z. Chen, “Denoising in electronic speckle pattern interferometry fringes by the filtering method based on partial differential equations,” Opt. Commun. 260, 91–96 (2006).

[CrossRef]

C. Tang, F. Zhang, and Z. Chen, “Contrast enhancement for electronic speckle pattern interferometry fringes by the differential equation enhancement method,” Appl. Opt. 45, 2287–2294 (2006).

[CrossRef]

T. I. Voronyak, A. B. Kmet’, and O. V. Lychak, “Single-step phase-shifting speckle interferometry,” Mater. Sci. 43, 554–567 (2007).

[CrossRef]

H. A. Aebischery and S. Waldner, “A simple and effective method for filtering speckle-interferometric phase fringe patterns,” Opt. Commun. 162, 205–210 (1999).

[CrossRef]

L. Cheng, C. Tang, S. Yan, X. Chen, L. Wang, and B. Wang, “New fourth-order partial differential equations for filtering in electronic speckle pattern interferometry fringes,” Opt. Commun. 284, 5549–5555 (2011).

[CrossRef]

L. Cheng, C. Tang, S. Yan, X. Chen, L. Wang, and B. Wang, “New fourth-order partial differential equations for filtering in electronic speckle pattern interferometry fringes,” Opt. Commun. 284, 5549–5555 (2011).

[CrossRef]

W. Lv, C. Tang, and W. Wang, “Noise reduction in electronic speckle pattern interferometry fringes by fourth-order partial differential equations,” Proc. SPIE 6279, (2007).

[CrossRef]

C. Tang, W. Lu, S. Chen, Z. Zhang, B. Li, W. Wang, and Lin Han, “Denoising by coupled partial differential equations and extracting phase by backpropagation neural networks for electronic speckle pattern interferometry,” Appl. Opt. 46, 7475–7484 (2007).

[CrossRef]

S. K. Weeratunga and C. Kamath, “A comparison of PDE based non-linear anisotropic diffusion techniques for image denoising,” Proc. SPIE 5014, 151493 (2003).

[CrossRef]

J. Weikert, Anisotropic Diffusion in Image Processing (Teubner Verlag, 1998).

A. P. Witkin, “Scale-space filtering,” in Proceedings of International Joint Conference on Artificial Intelligence (Morgan Kaufmann, 1983), pp. 1019–1021.

K. H. Womack, “Interferometric phase measurement using spatial synchronous detection,” Opt. Eng. 23, 391–395 (1984).

J. Wu and C. Tang, “PDE-based random-valued impulse noise removal based on new class of controlling functions,” IEEE Trans. Image Process. 20, 2428–2438 (2011).

[CrossRef]

C. Tang, F. Zhang, H. Yan, and Z. Chen, “Denoising in electronic speckle pattern interferometry fringes by the filtering method based on partial differential equations,” Opt. Commun. 260, 91–96 (2006).

[CrossRef]

L. Cheng, C. Tang, S. Yan, X. Chen, L. Wang, and B. Wang, “New fourth-order partial differential equations for filtering in electronic speckle pattern interferometry fringes,” Opt. Commun. 284, 5549–5555 (2011).

[CrossRef]

Y. You and M. Kaveh, “Fourth-order partial differential equations for noise removal,” IEEE Trans. Image Process. 9, 1723–1730 (2000).

[CrossRef]

C. Tang, F. Zhang, H. Yan, and Z. Chen, “Denoising in electronic speckle pattern interferometry fringes by the filtering method based on partial differential equations,” Opt. Commun. 260, 91–96 (2006).

[CrossRef]

C. Tang, F. Zhang, and Z. Chen, “Contrast enhancement for electronic speckle pattern interferometry fringes by the differential equation enhancement method,” Appl. Opt. 45, 2287–2294 (2006).

[CrossRef]

S. Nakadate and H. Saito, “Fringe scanning speckle-pattern interferometry,” Appl. Opt. 24, 2172–2180 (1985).

[CrossRef]

C. C. Kao, G. B. Yeh, S. S. Lee, C. K. Lee, C. S. Yang, and K. C. Wu, “Phase-shifting algorithms for electronic speckle pattern interferometry,” Appl. Opt. 41, 46–54 (2002).

[CrossRef]

C. Tang, F. Zhang, and Z. Chen, “Contrast enhancement for electronic speckle pattern interferometry fringes by the differential equation enhancement method,” Appl. Opt. 45, 2287–2294 (2006).

[CrossRef]

C. Tang, W. Lu, S. Chen, Z. Zhang, B. Li, W. Wang, and Lin Han, “Denoising by coupled partial differential equations and extracting phase by backpropagation neural networks for electronic speckle pattern interferometry,” Appl. Opt. 46, 7475–7484 (2007).

[CrossRef]

Y. Chen, C. A. Z. Barcelos, and B. A. Mairz, “Smoothing and edge detection by time-varying coupled nonlinear diffusion equations,” Comput. Vis. Image Understand. 82, 85–100 (2001).

[CrossRef]

M. Lysaker, A. Lundervold, and X.-C. Tai, “Noise removal using fourth-order partial differential equation with applications to medical magnetic resonance images in space and time,” IEEE Trans. Image Process 12, 1579–1590(2003).

[CrossRef]

G. Sapiro and D. L. Ringach, “Anisotropic diffusion of multivalued images with applications to color filtering,” IEEE Trans. Image Process 5, 1582–1586 (1996).

[CrossRef]

J. Wu and C. Tang, “PDE-based random-valued impulse noise removal based on new class of controlling functions,” IEEE Trans. Image Process. 20, 2428–2438 (2011).

[CrossRef]

Y. You and M. Kaveh, “Fourth-order partial differential equations for noise removal,” IEEE Trans. Image Process. 9, 1723–1730 (2000).

[CrossRef]

H. M. Salinas and D. C. Fernández, “Comparison of PDE-based nonlinear diffusion approaches for image enhancement and denoising in optical coherence tomography,” IEEE Trans. Med. Imaging 26, 761–771 (2007).

[CrossRef]

P. Perona and J. Malik, “Scale-space and edge detection using anisotropic diffusion,” IEEE Trans. Pattern Anal. Machine Intell. 12, 629–639 (1990).

[CrossRef]

T. I. Voronyak, A. B. Kmet’, and O. V. Lychak, “Single-step phase-shifting speckle interferometry,” Mater. Sci. 43, 554–567 (2007).

[CrossRef]

H. A. Aebischery and S. Waldner, “A simple and effective method for filtering speckle-interferometric phase fringe patterns,” Opt. Commun. 162, 205–210 (1999).

[CrossRef]

C. Tang, F. Zhang, H. Yan, and Z. Chen, “Denoising in electronic speckle pattern interferometry fringes by the filtering method based on partial differential equations,” Opt. Commun. 260, 91–96 (2006).

[CrossRef]

L. Cheng, C. Tang, S. Yan, X. Chen, L. Wang, and B. Wang, “New fourth-order partial differential equations for filtering in electronic speckle pattern interferometry fringes,” Opt. Commun. 284, 5549–5555 (2011).

[CrossRef]

K. H. Womack, “Interferometric phase measurement using spatial synchronous detection,” Opt. Eng. 23, 391–395 (1984).

X. Su and W. Chen, “Fourier transform profilometry: a review,” Opt. Lasers Eng. 35, 263–284 (2001).

[CrossRef]

H. Wang, Q. Kemao, W. Gao, F. Lin, and H. S. Seah, “Fringe pattern denoising using coherence enhancing diffusion,” Opt. Lett. 34, 1141–1143 (2009).

[CrossRef]

C. Tang, L. Han, H. Ren, D. Zhou, Y. Chang, X. Wang, and X. Cui, “Second-order oriented partial-differential equations for denoising in electronic-speckle-pattern interferometry fringes,” Opt. Lett. 33, 2179–2181 (2008).

[CrossRef]

L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Physica 60, 259–268 (1992).

[CrossRef]

S. K. Weeratunga and C. Kamath, “A comparison of PDE based non-linear anisotropic diffusion techniques for image denoising,” Proc. SPIE 5014, 151493 (2003).

[CrossRef]

W. Lv, C. Tang, and W. Wang, “Noise reduction in electronic speckle pattern interferometry fringes by fourth-order partial differential equations,” Proc. SPIE 6279, (2007).

[CrossRef]

F. Catté, P.-L. Lions, J.-M. Morel, and T. Coll, “Image selective smoothing and edge detection by nonlinear diffusion,” SIAM J. Numer. Anal. 29, 182–193 (1992).

[CrossRef]

L. Alvarez, P.-L. Lions, and J.-M. Morel, “Image selective smoothing and edge detection by nonlinear diffusion,” SIAM J. Numer. Anal. 29, 845–866 (1992).

[CrossRef]

Wikipedia, “Euler-Lagrange equation,” http://en.wikipedia.org/wiki/Euler%E2%80%93Lagrange_equation .

G. Sapiro, Geometric Partial Differential Equations and Image Analysis (Cambridge University, 2001).

A. P. Witkin, “Scale-space filtering,” in Proceedings of International Joint Conference on Artificial Intelligence (Morgan Kaufmann, 1983), pp. 1019–1021.

M. Aslan, “Toward the development of high-speed microscopic ESPI system for monitoring laser heating/drilling of alumina Al2O3 substrates,” Ph.D. dissertation (Pennsylvania State University, 2000).

J. Weikert, Anisotropic Diffusion in Image Processing (Teubner Verlag, 1998).