Abstract

We propose a denoising method for digital holography mod 2π wrapped phase map by using an adaptation of the SPArsity DEnoising of Digital Holograms (SPADEDH) algorithm. SPADEDH is a l1 minimization algorithm able to suppress the noise components on digital holograms without any prior knowledge or estimation about the statistics of noise. We test our algorithm with either general numerical simulated wrapped phase, quantifying the performance with different efficiency parameters and comparing it with two popular denoising strategies, i.e., median and Gaussian filters, and specific experimental tests, by focusing our attention on long-sequence wrapped quantitative phase maps (QPMs) of in vitro cells, which aim to have uncorrupted QPMs. In addition, we prove that the proposed algorithm can be used as a helper for the typical local phase unwrapping algorithms.

© 2013 Optical Society of America

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    [CrossRef]

2012

X. Yu, M. Cross, C. Liu, D. C. Clark, D. T. Haynie, and M. K. Kim, “Measurement of the traction force of biological cells by digital holography,” Biomed. Opt. Express 3, 153–159 (2012).
[CrossRef]

J. F. Restrepo and J. Garcia-Sucerquia, “Automatic three-dimensional tracking of particles with high-numerical-aperture digital lensless holographic microscopy,” Opt. Lett. 37, 752–754 (2012).
[CrossRef]

M. Paturzo, A. Finizio, P. Memmolo, R. Puglisi, D. Balduzzi, A. Galli, and P. Ferraro, “Microscopy imaging and quantitative phase contrast mapping in turbid microfluidic channels by digital holography,” Lab Chip 12, 3073–3076 (2012).
[CrossRef]

Y. H. Huang Howard, L. Tian, Z. Zhang, Y. Liu, Z. Chen, and G. Barbastathis, “Path-independent phase unwrapping using phase gradient and total-variation (TV) denoising,” Opt. Express 20, 14075–14089 (2012).
[CrossRef]

M. A. Navarro, J. C. Estrada, M. Servin, J. A. Quiroga, and J. Vargas, “Fast two-dimensional simultaneous phase unwrapping and low-pass filtering,” Opt. Express 20, 2556–2561 (2012).
[CrossRef]

J. F. Weng and Y. L. Lo, “Integration of robust filters and phase unwrapping algorithms for image reconstruction of objects containing height discontinuities,” Opt. Express 20, 10896–10920 (2012).
[CrossRef]

P. Memmolo, I. Esnaola, A. Finizio, M. Paturzo, P. Ferraro, and A. M. Tulino, “SPADEDH: a sparsity-based denoising method of digital holograms without knowing the noise statistics,” Opt. Express 20, 17250–17257 (2012).
[CrossRef]

2011

2010

2009

M. Gdeisat, M. Arevalillo-Herráez, D. Burton, and F. Lilley, “Three-dimensional phase unwrapping using the Hungarian algorithm,” Opt. Lett. 34, 2994–2996 (2009).
[CrossRef]

N. T. Shaked, M. T. Rinehart, and A. Wax, “Dual-interference-channel quantitative-phase microscopy of live cell dynamics,” Opt. Lett. 34, 767–769 (2009).
[CrossRef]

P. Langehanenberg, L. Ivanova, I. Bernhardt, S. Ketelhut, A. Vollmer, D. Dirksen, G. Georgiev, G. von Bally, and B. Kemper, “Automated three-dimensional tracking of living cells by digital holographic microscopy,” J. Biomed. Opt. 14, 014018 (2009).
[CrossRef]

2008

2007

R. Yamaki and A. Hirose, “Singularity-spreading phase unwrapping,” IEEE Trans. Geosci. Remote Sens. 45, 3240–3251 (2007).
[CrossRef]

2004

2002

Z. Wang and A. C. Bovik, “A universal image quality index,” IEEE Signal Process. Lett. 9, 81–84 (2002).
[CrossRef]

1999

1998

1997

1988

R. M. Goldstein, H. A. Zebken, and C. L. Werner, “Satellite radar interferometry: two-dimensional phase unwrapping,” Radio Sci. 23, 713 (1988).
[CrossRef]

1985

R. T. Franceschi, W. M. James, and G. Zerlauth, “1 alpha, 25-dihydroxyvitamin D3 specific regulation of growth, morphology, and fibronectin in a human osteosarcoma cell line,” J. Cell. Physiol. 123, 401–409 (1985).
[CrossRef]

Anand, A.

Arevalillo-Herráez, M.

Astola, J.

Asundi, A.

Balduzzi, D.

M. Paturzo, A. Finizio, P. Memmolo, R. Puglisi, D. Balduzzi, A. Galli, and P. Ferraro, “Microscopy imaging and quantitative phase contrast mapping in turbid microfluidic channels by digital holography,” Lab Chip 12, 3073–3076 (2012).
[CrossRef]

Barbastathis, G.

Bernhardt, I.

P. Langehanenberg, L. Ivanova, I. Bernhardt, S. Ketelhut, A. Vollmer, D. Dirksen, G. Georgiev, G. von Bally, and B. Kemper, “Automated three-dimensional tracking of living cells by digital holographic microscopy,” J. Biomed. Opt. 14, 014018 (2009).
[CrossRef]

Bioucas-Dias, J.

Bishara, W.

Bovik, A. C.

Z. Wang and A. C. Bovik, “A universal image quality index,” IEEE Signal Process. Lett. 9, 81–84 (2002).
[CrossRef]

Burton, D.

Chen, X.-J.

Chen, Z.

Clark, D. C.

Cross, M.

Daneshpanah, M.

Dirksen, D.

P. Langehanenberg, L. Ivanova, I. Bernhardt, S. Ketelhut, A. Vollmer, D. Dirksen, G. Georgiev, G. von Bally, and B. Kemper, “Automated three-dimensional tracking of living cells by digital holographic microscopy,” J. Biomed. Opt. 14, 014018 (2009).
[CrossRef]

Donoho, D.

D. Donoho, Y. Tsaig, I. Drori, and J-L. Starck, “Sparse solution of underdetermined linear equations by stagewise orthogonal matching pursuit,” Stanford Tech. Rep. (Stanford University, 2006), pp. 1–39.

Drori, I.

D. Donoho, Y. Tsaig, I. Drori, and J-L. Starck, “Sparse solution of underdetermined linear equations by stagewise orthogonal matching pursuit,” Stanford Tech. Rep. (Stanford University, 2006), pp. 1–39.

Egiazarian, K.

Elad, M.

M. Elad, M. A. T. Figueiredo, and M. Yi, “On the role of sparse and redundant representations in image processing,” Proc. IEEE 98, 972–982 (2010).
[CrossRef]

Esnaola, I.

Estrada, J. C.

Ferraro, P.

Fessler, J. A.

Figueiredo, M. A. T.

M. Elad, M. A. T. Figueiredo, and M. Yi, “On the role of sparse and redundant representations in image processing,” Proc. IEEE 98, 972–982 (2010).
[CrossRef]

Finizio, A.

Fornaro, G.

Franceschetti, G.

Franceschi, R. T.

R. T. Franceschi, W. M. James, and G. Zerlauth, “1 alpha, 25-dihydroxyvitamin D3 specific regulation of growth, morphology, and fibronectin in a human osteosarcoma cell line,” J. Cell. Physiol. 123, 401–409 (1985).
[CrossRef]

Galli, A.

M. Paturzo, A. Finizio, P. Memmolo, R. Puglisi, D. Balduzzi, A. Galli, and P. Ferraro, “Microscopy imaging and quantitative phase contrast mapping in turbid microfluidic channels by digital holography,” Lab Chip 12, 3073–3076 (2012).
[CrossRef]

Garcia-Sucerquia, J.

Gdeisat, M.

Georgiev, G.

P. Langehanenberg, L. Ivanova, I. Bernhardt, S. Ketelhut, A. Vollmer, D. Dirksen, G. Georgiev, G. von Bally, and B. Kemper, “Automated three-dimensional tracking of living cells by digital holographic microscopy,” J. Biomed. Opt. 14, 014018 (2009).
[CrossRef]

Ghiglia, D. C.

D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms and Software (Wiley-Interscience, 1998).

Gisselsson, D.

D. Gisselsson, Y. Jin, D. Lindgren, J. Persson, L. Gisselsson, S. Hanks, D. Sehic, L. H. Mengelbier, I. Øra, N. Rahman, F. Mertens, F. Mitelman, and N. Mandahl, “Generation of trisomies in cancer cells by multipolar mitosis and incomplete cytokinesis,” Proc. Natl. Acad. Sci. USA 107, 20489–20493 (2010).
[CrossRef]

Gisselsson, L.

D. Gisselsson, Y. Jin, D. Lindgren, J. Persson, L. Gisselsson, S. Hanks, D. Sehic, L. H. Mengelbier, I. Øra, N. Rahman, F. Mertens, F. Mitelman, and N. Mandahl, “Generation of trisomies in cancer cells by multipolar mitosis and incomplete cytokinesis,” Proc. Natl. Acad. Sci. USA 107, 20489–20493 (2010).
[CrossRef]

Goldstein, R. M.

R. M. Goldstein, H. A. Zebken, and C. L. Werner, “Satellite radar interferometry: two-dimensional phase unwrapping,” Radio Sci. 23, 713 (1988).
[CrossRef]

Hanks, S.

D. Gisselsson, Y. Jin, D. Lindgren, J. Persson, L. Gisselsson, S. Hanks, D. Sehic, L. H. Mengelbier, I. Øra, N. Rahman, F. Mertens, F. Mitelman, and N. Mandahl, “Generation of trisomies in cancer cells by multipolar mitosis and incomplete cytokinesis,” Proc. Natl. Acad. Sci. USA 107, 20489–20493 (2010).
[CrossRef]

Haynie, D. T.

Heshmat, S.

Hirose, A.

R. Yamaki and A. Hirose, “Singularity-spreading phase unwrapping,” IEEE Trans. Geosci. Remote Sens. 45, 3240–3251 (2007).
[CrossRef]

Howard, Y. H. Huang

Huang, Y. H.

Hung, Y. Y.

Ivanova, L.

P. Langehanenberg, L. Ivanova, I. Bernhardt, S. Ketelhut, A. Vollmer, D. Dirksen, G. Georgiev, G. von Bally, and B. Kemper, “Automated three-dimensional tracking of living cells by digital holographic microscopy,” J. Biomed. Opt. 14, 014018 (2009).
[CrossRef]

James, W. M.

R. T. Franceschi, W. M. James, and G. Zerlauth, “1 alpha, 25-dihydroxyvitamin D3 specific regulation of growth, morphology, and fibronectin in a human osteosarcoma cell line,” J. Cell. Physiol. 123, 401–409 (1985).
[CrossRef]

Janabi-Sharifi, F.

Javidi, B.

Jin, Y.

D. Gisselsson, Y. Jin, D. Lindgren, J. Persson, L. Gisselsson, S. Hanks, D. Sehic, L. H. Mengelbier, I. Øra, N. Rahman, F. Mertens, F. Mitelman, and N. Mandahl, “Generation of trisomies in cancer cells by multipolar mitosis and incomplete cytokinesis,” Proc. Natl. Acad. Sci. USA 107, 20489–20493 (2010).
[CrossRef]

Kassim, A. A.

D. Zonoobi, A. A. Kassim, and Y. V. Venkatesh, “Gini index as sparsity measure for signal reconstruction from compressive samples,” IEEE J. Select. Topics Signal Process. 5, 927–932 (2011).
[CrossRef]

Katkovnik, V.

Kemper, B.

P. Langehanenberg, L. Ivanova, I. Bernhardt, S. Ketelhut, A. Vollmer, D. Dirksen, G. Georgiev, G. von Bally, and B. Kemper, “Automated three-dimensional tracking of living cells by digital holographic microscopy,” J. Biomed. Opt. 14, 014018 (2009).
[CrossRef]

Ketelhut, S.

P. Langehanenberg, L. Ivanova, I. Bernhardt, S. Ketelhut, A. Vollmer, D. Dirksen, G. Georgiev, G. von Bally, and B. Kemper, “Automated three-dimensional tracking of living cells by digital holographic microscopy,” J. Biomed. Opt. 14, 014018 (2009).
[CrossRef]

Kim, M. K.

Lanari, R.

Langehanenberg, P.

P. Langehanenberg, L. Ivanova, I. Bernhardt, S. Ketelhut, A. Vollmer, D. Dirksen, G. Georgiev, G. von Bally, and B. Kemper, “Automated three-dimensional tracking of living cells by digital holographic microscopy,” J. Biomed. Opt. 14, 014018 (2009).
[CrossRef]

Li, H.

Li, Y.-H.

Lilley, F.

Lindgren, D.

D. Gisselsson, Y. Jin, D. Lindgren, J. Persson, L. Gisselsson, S. Hanks, D. Sehic, L. H. Mengelbier, I. Øra, N. Rahman, F. Mertens, F. Mitelman, and N. Mandahl, “Generation of trisomies in cancer cells by multipolar mitosis and incomplete cytokinesis,” Proc. Natl. Acad. Sci. USA 107, 20489–20493 (2010).
[CrossRef]

Liu, C.

Liu, Y.

Lo, Y. L.

Luo, Z.-Y.

Mandahl, N.

D. Gisselsson, Y. Jin, D. Lindgren, J. Persson, L. Gisselsson, S. Hanks, D. Sehic, L. H. Mengelbier, I. Øra, N. Rahman, F. Mertens, F. Mitelman, and N. Mandahl, “Generation of trisomies in cancer cells by multipolar mitosis and incomplete cytokinesis,” Proc. Natl. Acad. Sci. USA 107, 20489–20493 (2010).
[CrossRef]

Memmolo, P.

Mengelbier, L. H.

D. Gisselsson, Y. Jin, D. Lindgren, J. Persson, L. Gisselsson, S. Hanks, D. Sehic, L. H. Mengelbier, I. Øra, N. Rahman, F. Mertens, F. Mitelman, and N. Mandahl, “Generation of trisomies in cancer cells by multipolar mitosis and incomplete cytokinesis,” Proc. Natl. Acad. Sci. USA 107, 20489–20493 (2010).
[CrossRef]

Mertens, F.

D. Gisselsson, Y. Jin, D. Lindgren, J. Persson, L. Gisselsson, S. Hanks, D. Sehic, L. H. Mengelbier, I. Øra, N. Rahman, F. Mertens, F. Mitelman, and N. Mandahl, “Generation of trisomies in cancer cells by multipolar mitosis and incomplete cytokinesis,” Proc. Natl. Acad. Sci. USA 107, 20489–20493 (2010).
[CrossRef]

Miccio, L.

Mitelman, F.

D. Gisselsson, Y. Jin, D. Lindgren, J. Persson, L. Gisselsson, S. Hanks, D. Sehic, L. H. Mengelbier, I. Øra, N. Rahman, F. Mertens, F. Mitelman, and N. Mandahl, “Generation of trisomies in cancer cells by multipolar mitosis and incomplete cytokinesis,” Proc. Natl. Acad. Sci. USA 107, 20489–20493 (2010).
[CrossRef]

Miyamoto, N.

Navarro, M. A.

Nishiyama, S.

Øra, I.

D. Gisselsson, Y. Jin, D. Lindgren, J. Persson, L. Gisselsson, S. Hanks, D. Sehic, L. H. Mengelbier, I. Øra, N. Rahman, F. Mertens, F. Mitelman, and N. Mandahl, “Generation of trisomies in cancer cells by multipolar mitosis and incomplete cytokinesis,” Proc. Natl. Acad. Sci. USA 107, 20489–20493 (2010).
[CrossRef]

Ozcan, A.

Paturzo, M.

Persson, J.

D. Gisselsson, Y. Jin, D. Lindgren, J. Persson, L. Gisselsson, S. Hanks, D. Sehic, L. H. Mengelbier, I. Øra, N. Rahman, F. Mertens, F. Mitelman, and N. Mandahl, “Generation of trisomies in cancer cells by multipolar mitosis and incomplete cytokinesis,” Proc. Natl. Acad. Sci. USA 107, 20489–20493 (2010).
[CrossRef]

Pritt, M. D.

D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms and Software (Wiley-Interscience, 1998).

Puglisi, R.

M. Paturzo, A. Finizio, P. Memmolo, R. Puglisi, D. Balduzzi, A. Galli, and P. Ferraro, “Microscopy imaging and quantitative phase contrast mapping in turbid microfluidic channels by digital holography,” Lab Chip 12, 3073–3076 (2012).
[CrossRef]

Qu, S.-L.

Quiroga, J. A.

Rahman, N.

D. Gisselsson, Y. Jin, D. Lindgren, J. Persson, L. Gisselsson, S. Hanks, D. Sehic, L. H. Mengelbier, I. Øra, N. Rahman, F. Mertens, F. Mitelman, and N. Mandahl, “Generation of trisomies in cancer cells by multipolar mitosis and incomplete cytokinesis,” Proc. Natl. Acad. Sci. USA 107, 20489–20493 (2010).
[CrossRef]

Restrepo, J. F.

Rinehart, M. T.

Sansosti, E.

Schmidt, J. D.

Sehic, D.

D. Gisselsson, Y. Jin, D. Lindgren, J. Persson, L. Gisselsson, S. Hanks, D. Sehic, L. H. Mengelbier, I. Øra, N. Rahman, F. Mertens, F. Mitelman, and N. Mandahl, “Generation of trisomies in cancer cells by multipolar mitosis and incomplete cytokinesis,” Proc. Natl. Acad. Sci. USA 107, 20489–20493 (2010).
[CrossRef]

Servin, M.

Shaked, N. T.

Shin, D.

Sotthivirat, S.

Starck, J-L.

D. Donoho, Y. Tsaig, I. Drori, and J-L. Starck, “Sparse solution of underdetermined linear equations by stagewise orthogonal matching pursuit,” Stanford Tech. Rep. (Stanford University, 2006), pp. 1–39.

Strand, J.

Taxt, T.

Tesauro, M.

Tian, L.

Tomioka, S.

Tsaig, Y.

D. Donoho, Y. Tsaig, I. Drori, and J-L. Starck, “Sparse solution of underdetermined linear equations by stagewise orthogonal matching pursuit,” Stanford Tech. Rep. (Stanford University, 2006), pp. 1–39.

Tulino, A. M.

Vargas, J.

Venema, T. M.

Venkatesh, Y. V.

D. Zonoobi, A. A. Kassim, and Y. V. Venkatesh, “Gini index as sparsity measure for signal reconstruction from compressive samples,” IEEE J. Select. Topics Signal Process. 5, 927–932 (2011).
[CrossRef]

Vollmer, A.

P. Langehanenberg, L. Ivanova, I. Bernhardt, S. Ketelhut, A. Vollmer, D. Dirksen, G. Georgiev, G. von Bally, and B. Kemper, “Automated three-dimensional tracking of living cells by digital holographic microscopy,” J. Biomed. Opt. 14, 014018 (2009).
[CrossRef]

von Bally, G.

P. Langehanenberg, L. Ivanova, I. Bernhardt, S. Ketelhut, A. Vollmer, D. Dirksen, G. Georgiev, G. von Bally, and B. Kemper, “Automated three-dimensional tracking of living cells by digital holographic microscopy,” J. Biomed. Opt. 14, 014018 (2009).
[CrossRef]

Wang, Z.

Z. Wang and A. C. Bovik, “A universal image quality index,” IEEE Signal Process. Lett. 9, 81–84 (2002).
[CrossRef]

Wax, A.

Weng, J. F.

Wensen, Zhou

Werner, C. L.

R. M. Goldstein, H. A. Zebken, and C. L. Werner, “Satellite radar interferometry: two-dimensional phase unwrapping,” Radio Sci. 23, 713 (1988).
[CrossRef]

Yamaki, R.

R. Yamaki and A. Hirose, “Singularity-spreading phase unwrapping,” IEEE Trans. Geosci. Remote Sens. 45, 3240–3251 (2007).
[CrossRef]

Yi, M.

M. Elad, M. A. T. Figueiredo, and M. Yi, “On the role of sparse and redundant representations in image processing,” Proc. IEEE 98, 972–982 (2010).
[CrossRef]

Yu, X.

Zebken, H. A.

R. M. Goldstein, H. A. Zebken, and C. L. Werner, “Satellite radar interferometry: two-dimensional phase unwrapping,” Radio Sci. 23, 713 (1988).
[CrossRef]

Zerlauth, G.

R. T. Franceschi, W. M. James, and G. Zerlauth, “1 alpha, 25-dihydroxyvitamin D3 specific regulation of growth, morphology, and fibronectin in a human osteosarcoma cell line,” J. Cell. Physiol. 123, 401–409 (1985).
[CrossRef]

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Supplementary Material (2)

» Media 1: AVI (2145 KB)     
» Media 2: AVI (919 KB)     

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Figures (6)

Fig. 1.
Fig. 1.

Results of the proposed method on the two test cases. (a), (e) are the noisy phase map. (b), (f) are the sparse representation of (a), (e) using Eq. (3). (c), (g) are the outputs of the proposed algorithm. (d), (h) are the recovered phase maps.

Fig. 2.
Fig. 2.

Evaluation of the efficiency parameters, for the three compared method, for the examples reported in Figs. 1(a) and 1(e). In the first column (a), (c), (e) are reported the Q value, the PSNR, the evaluation of bias, obtained for the case reported in Fig. 1(a), varying the standard deviation of noise. In the second column (b), (d), (f) there are the corresponding parameters evaluated for the case in Fig. 1(e). In (g), (h) we report a comparison between the profiles of the compared methods and the ideal case for the examples in Figs. 1(a) and 1(e), respectively.

Fig. 3.
Fig. 3.

(a), (c) are the unwrapped phase maps for the ideal simulated examples reported in Fig. 1. (b), (d) are unwrapped phase images obtained from the denoised wrapped maps shown in Figs. 1(d) and 1(h), respectively. In (e) we report the Q value as a function of the standard deviation of noise, for both examples, after the unwrapping steps.

Fig. 4.
Fig. 4.

(a) Original wrapped phase map. (b) Denoised phase obtained using the proposed algorithm. (c), (d) are the unwrapped phase maps, using the flood-fill PUA, obtained from (a), (b), respectively. In (e), (f) we report a vertical profiles extracted from the noisy and denoised phase maps for both wrapped and unwrapped cases, respectively.

Fig. 5.
Fig. 5.

(a) Original wrapped phase map. (b) Denoised phase obtained using the proposed algorithm. (c), (d) are the unwrapped phase maps, using flood-fill PUA, obtained from (a), (b), respectively. In (e), (f) we report an horizontal profiles extracted from the noisy and denoised phase maps for both wrapped and unwrapped cases, respectively. Media 1 shows the entire sequence analyzed.

Fig. 6.
Fig. 6.

(a) Original wrapped phase map. (b) Denoised phase obtained using the proposed algorithm. (c), (d) are the unwrapped phase maps, using Goldstein’s PUA, obtained from (a), (b), respectively. In (e), (f) we report an horizontal profiles extracted from the noisy and denoised phase maps for both wrapped and unwrapped cases, respectively. Media 2 shows selected frames of the entire analyzed sequence.

Equations (5)

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vden=argminv1s.t.Fδ{h˜}=v,
vden=argminv1s.t.Φ{p˜}=v,
Φ{x}=FFT{exp(ix)},
pden=arg{IFFT{vden}}
Q=cov(p,pden)σ(p)σ(pden)·2E(p)E(pden)E2(p)+E2(pden)·2σ(p)σ(pden)σ2(p)+σ2(pden),

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