Abstract

Division of focal plane (DoFP) polarimeters are composed of interlaced linear polarizers overlaid upon a focal plane array sensor. The interpolation is essential to reconstruct polarization information. However, current interpolation methods are based on the unrealistic assumption of noise-free images. Thus, it is advantageous to carry out denoising before interpolation. In this paper, we propose a principle component analysis (PCA) based denoising method, which works directly on DoFP images. Both simulated and real DoFP images are used to evaluate the denoising performance. Experimental results show that the proposed method can effectively suppress noise while preserving edges.

© 2017 Optical Society of America

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References

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    [Crossref] [PubMed]
  5. S. Alali and A. Vitkin, “Polarized light imaging in biomedicine: emerging Mueller matrix methodologies for bulk tissue assessment,” J. Biomed. Opt. 20(6), 061104 (2015).
    [Crossref]
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    [Crossref]
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2016 (2)

2015 (4)

Z. Chen, X. Wang, and R. Liang, “Snapshot phase shift fringe projection 3D surface measurement,” Opt. Express 23(2), 667–673 (2015).
[Crossref] [PubMed]

S. Alali and A. Vitkin, “Polarized light imaging in biomedicine: emerging Mueller matrix methodologies for bulk tissue assessment,” J. Biomed. Opt. 20(6), 061104 (2015).
[Crossref]

B. Kunnen, C. Macdonald, A. Doronin, S. Jacques, M. Eccles, and I. Meglinski, “Application of circularly polarized light for non-invasive diagnosis of cancerous tissues and turbid tissue-like scattering media,” J. Biophotonics 8(4), 317–323 (2015).
[Crossref]

T. Mu, C. Zhang, and R. Liang, “Demonstration of a snapshot full-Stokes division-of-aperture imaging polarimeter using Wollaston prism array,” J. Opt. 17(12), 125708 (2015).
[Crossref]

2014 (2)

2013 (2)

S. Gao and V. Gruev, “Gradient-based interpolation method for division of focal plane polarimeters,” Opt. Express 21(1), 1137–1151 (2013).
[Crossref] [PubMed]

G. Liu, Z. Lin, S. Yan, J. Sun, Y. Yu, and Y. Ma, “Robust Recovery of Subspace Structures by Low-Rank Representation,” IEEE Trans. Pattern Anal. Machine Intel. 35(1), 171–184 (2013).
[Crossref]

2012 (1)

2011 (4)

T. Krishna, C. Creusere, and D. Voelz, “Passive polarimetric imagery-based material classification robust to illumination source position and viewpoint,” IEEE Trans. Image Process. 20(1), 288–292 (2011).
[Crossref]

S. Gao and V. Gruev, “Image interpolation methods evaluation for division of focal plane polarimeters,” Proc. SPIE 8012, 80120N (2011).
[Crossref]

A. Pierangelo, A. Benali, M. R. Antonelli, T. Novikova, P. Validire, B. Gayet, and A. De Martino, “Ex-vivo characterization of human colon cancer by Mueller polarimetric imaging,” Opt. Express 19(2), 1582–1593 (2011).
[Crossref] [PubMed]

S. Gao and V. Gruev, “Bilinear and bicubic interpolation methods for division of focal plane polarimeters,” Opt. Express 19(27), 26161–26173 (2011).
[Crossref]

2010 (1)

L. Zhang, W. Dong, D. Zhang, and G. Shi, “Two-stage image denoising by principal component analysis with local pixel grouping,” Pattern Recogn. 43(4), 1531–1549 (2010).
[Crossref]

2009 (3)

L. Zhang, R. Lukac, X. Wu, and D. Zhang, “PCA-Based Spatially Adaptive Denoising of CFA Images for Single-Sensor Digital Cameras,” IEEE Trans. Image Process. 18(4), 2419–2434 (2009).

A. Beck and M. Teboulle, “Fast Gradient-Based Algorithms for Constrained Total Variation Image Denoising and Deblurring Problems,” IEEE Trans. Image Process. 18(11), 2419–2434 (2009).
[Crossref] [PubMed]

B. Ratliff, C. LaCasse, and S. Tyo, “Interpolation strategies for reducing IFoV artifacts in microgrid polarimeter imagery,” Opt. Express 17(11), 9112–9125 (2009).
[Crossref] [PubMed]

2006 (3)

2000 (1)

S. Chang, B. Yu, and M. Vetterli, “Spatially adaptive wavelet thresholding with context modeling for image denoising,” IEEE Trans. Image Process. 9(9), 1522–1531 (2000).
[Crossref]

1994 (1)

D. L. Donoho and I. M. Johnstone, “Ideal spatial adaptation by wavelet shrinkage,” Biometrika,  81(3), 425–455 (1994).
[Crossref]

Aharon, M.

M. Elad and M. Aharon, “Image denoising via sparse and redundant representations over learned dictionaries,” IEEE Trans. Image Process. 15(20), 3736–3745 (2006).
[Crossref] [PubMed]

Alali, S.

S. Alali and A. Vitkin, “Polarized light imaging in biomedicine: emerging Mueller matrix methodologies for bulk tissue assessment,” J. Biomed. Opt. 20(6), 061104 (2015).
[Crossref]

Antonelli, M. R.

Beck, A.

A. Beck and M. Teboulle, “Fast Gradient-Based Algorithms for Constrained Total Variation Image Denoising and Deblurring Problems,” IEEE Trans. Image Process. 18(11), 2419–2434 (2009).
[Crossref] [PubMed]

Benali, A.

Bevington, Philip R.

Philip R. Bevington and D. Keith Robinson, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, New York, 1992).

Brock, N.

Chang, S.

S. Chang, B. Yu, and M. Vetterli, “Spatially adaptive wavelet thresholding with context modeling for image denoising,” IEEE Trans. Image Process. 9(9), 1522–1531 (2000).
[Crossref]

Chang, Z.

Chen, C.

Chen, Z.

Chenault, D. B.

Chipman, R. A.

Creusere, C.

T. Krishna, C. Creusere, and D. Voelz, “Passive polarimetric imagery-based material classification robust to illumination source position and viewpoint,” IEEE Trans. Image Process. 20(1), 288–292 (2011).
[Crossref]

Cunningham, J. P.

De Martino, A.

Dong, W.

L. Zhang, W. Dong, D. Zhang, and G. Shi, “Two-stage image denoising by principal component analysis with local pixel grouping,” Pattern Recogn. 43(4), 1531–1549 (2010).
[Crossref]

Donoho, D. L.

D. L. Donoho and I. M. Johnstone, “Ideal spatial adaptation by wavelet shrinkage,” Biometrika,  81(3), 425–455 (1994).
[Crossref]

Doronin, A.

B. Kunnen, C. Macdonald, A. Doronin, S. Jacques, M. Eccles, and I. Meglinski, “Application of circularly polarized light for non-invasive diagnosis of cancerous tissues and turbid tissue-like scattering media,” J. Biophotonics 8(4), 317–323 (2015).
[Crossref]

Eccles, M.

B. Kunnen, C. Macdonald, A. Doronin, S. Jacques, M. Eccles, and I. Meglinski, “Application of circularly polarized light for non-invasive diagnosis of cancerous tissues and turbid tissue-like scattering media,” J. Biophotonics 8(4), 317–323 (2015).
[Crossref]

Elad, M.

M. Elad and M. Aharon, “Image denoising via sparse and redundant representations over learned dictionaries,” IEEE Trans. Image Process. 15(20), 3736–3745 (2006).
[Crossref] [PubMed]

Fang, S.

Gao, S.

Gayet, B.

Gilboa, E.

Goldstein, D. L.

Gruev, V.

Hsu, W.

Hui, B.

Huo, X.

Jacques, S.

B. Kunnen, C. Macdonald, A. Doronin, S. Jacques, M. Eccles, and I. Meglinski, “Application of circularly polarized light for non-invasive diagnosis of cancerous tissues and turbid tissue-like scattering media,” J. Biophotonics 8(4), 317–323 (2015).
[Crossref]

Johnstone, I. M.

D. L. Donoho and I. M. Johnstone, “Ideal spatial adaptation by wavelet shrinkage,” Biometrika,  81(3), 425–455 (1994).
[Crossref]

Keith Robinson, D.

Philip R. Bevington and D. Keith Robinson, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, New York, 1992).

Krishna, T.

T. Krishna, C. Creusere, and D. Voelz, “Passive polarimetric imagery-based material classification robust to illumination source position and viewpoint,” IEEE Trans. Image Process. 20(1), 288–292 (2011).
[Crossref]

Kunnen, B.

B. Kunnen, C. Macdonald, A. Doronin, S. Jacques, M. Eccles, and I. Meglinski, “Application of circularly polarized light for non-invasive diagnosis of cancerous tissues and turbid tissue-like scattering media,” J. Biophotonics 8(4), 317–323 (2015).
[Crossref]

LaCasse, C.

Liang, R.

T. Mu, C. Zhang, and R. Liang, “Demonstration of a snapshot full-Stokes division-of-aperture imaging polarimeter using Wollaston prism array,” J. Opt. 17(12), 125708 (2015).
[Crossref]

Z. Chen, X. Wang, and R. Liang, “Snapshot phase shift fringe projection 3D surface measurement,” Opt. Express 23(2), 667–673 (2015).
[Crossref] [PubMed]

Lin, Z.

G. Liu, Z. Lin, S. Yan, J. Sun, Y. Yu, and Y. Ma, “Robust Recovery of Subspace Structures by Low-Rank Representation,” IEEE Trans. Pattern Anal. Machine Intel. 35(1), 171–184 (2013).
[Crossref]

Liu, G.

G. Liu, Z. Lin, S. Yan, J. Sun, Y. Yu, and Y. Ma, “Robust Recovery of Subspace Structures by Low-Rank Representation,” IEEE Trans. Pattern Anal. Machine Intel. 35(1), 171–184 (2013).
[Crossref]

Lukac, R.

L. Zhang, R. Lukac, X. Wu, and D. Zhang, “PCA-Based Spatially Adaptive Denoising of CFA Images for Single-Sensor Digital Cameras,” IEEE Trans. Image Process. 18(4), 2419–2434 (2009).

Luo, H.

Ma, Y.

G. Liu, Z. Lin, S. Yan, J. Sun, Y. Yu, and Y. Ma, “Robust Recovery of Subspace Structures by Low-Rank Representation,” IEEE Trans. Pattern Anal. Machine Intel. 35(1), 171–184 (2013).
[Crossref]

Macdonald, C.

B. Kunnen, C. Macdonald, A. Doronin, S. Jacques, M. Eccles, and I. Meglinski, “Application of circularly polarized light for non-invasive diagnosis of cancerous tissues and turbid tissue-like scattering media,” J. Biophotonics 8(4), 317–323 (2015).
[Crossref]

Meglinski, I.

B. Kunnen, C. Macdonald, A. Doronin, S. Jacques, M. Eccles, and I. Meglinski, “Application of circularly polarized light for non-invasive diagnosis of cancerous tissues and turbid tissue-like scattering media,” J. Biophotonics 8(4), 317–323 (2015).
[Crossref]

Mu, T.

T. Mu, C. Zhang, and R. Liang, “Demonstration of a snapshot full-Stokes division-of-aperture imaging polarimeter using Wollaston prism array,” J. Opt. 17(12), 125708 (2015).
[Crossref]

Myhre, G.

Nehorai, A.

Novikova, T.

Pau, S.

Peinado, A.

Pierangelo, A.

Ratliff, B.

Shaw, J. A.

Shi, G.

L. Zhang, W. Dong, D. Zhang, and G. Shi, “Two-stage image denoising by principal component analysis with local pixel grouping,” Pattern Recogn. 43(4), 1531–1549 (2010).
[Crossref]

Sun, J.

G. Liu, Z. Lin, S. Yan, J. Sun, Y. Yu, and Y. Ma, “Robust Recovery of Subspace Structures by Low-Rank Representation,” IEEE Trans. Pattern Anal. Machine Intel. 35(1), 171–184 (2013).
[Crossref]

Teboulle, M.

A. Beck and M. Teboulle, “Fast Gradient-Based Algorithms for Constrained Total Variation Image Denoising and Deblurring Problems,” IEEE Trans. Image Process. 18(11), 2419–2434 (2009).
[Crossref] [PubMed]

Tyo, J. S.

Tyo, S.

Validire, P.

Vetterli, M.

S. Chang, B. Yu, and M. Vetterli, “Spatially adaptive wavelet thresholding with context modeling for image denoising,” IEEE Trans. Image Process. 9(9), 1522–1531 (2000).
[Crossref]

Vitkin, A.

S. Alali and A. Vitkin, “Polarized light imaging in biomedicine: emerging Mueller matrix methodologies for bulk tissue assessment,” J. Biomed. Opt. 20(6), 061104 (2015).
[Crossref]

Voelz, D.

T. Krishna, C. Creusere, and D. Voelz, “Passive polarimetric imagery-based material classification robust to illumination source position and viewpoint,” IEEE Trans. Image Process. 20(1), 288–292 (2011).
[Crossref]

Wang, X.

Wu, X.

L. Zhang, R. Lukac, X. Wu, and D. Zhang, “PCA-Based Spatially Adaptive Denoising of CFA Images for Single-Sensor Digital Cameras,” IEEE Trans. Image Process. 18(4), 2419–2434 (2009).

Xia, X.

Yan, S.

G. Liu, Z. Lin, S. Yan, J. Sun, Y. Yu, and Y. Ma, “Robust Recovery of Subspace Structures by Low-Rank Representation,” IEEE Trans. Pattern Anal. Machine Intel. 35(1), 171–184 (2013).
[Crossref]

Yu, B.

S. Chang, B. Yu, and M. Vetterli, “Spatially adaptive wavelet thresholding with context modeling for image denoising,” IEEE Trans. Image Process. 9(9), 1522–1531 (2000).
[Crossref]

Yu, Y.

G. Liu, Z. Lin, S. Yan, J. Sun, Y. Yu, and Y. Ma, “Robust Recovery of Subspace Structures by Low-Rank Representation,” IEEE Trans. Pattern Anal. Machine Intel. 35(1), 171–184 (2013).
[Crossref]

Zhang, C.

T. Mu, C. Zhang, and R. Liang, “Demonstration of a snapshot full-Stokes division-of-aperture imaging polarimeter using Wollaston prism array,” J. Opt. 17(12), 125708 (2015).
[Crossref]

Zhang, D.

L. Zhang, W. Dong, D. Zhang, and G. Shi, “Two-stage image denoising by principal component analysis with local pixel grouping,” Pattern Recogn. 43(4), 1531–1549 (2010).
[Crossref]

L. Zhang, R. Lukac, X. Wu, and D. Zhang, “PCA-Based Spatially Adaptive Denoising of CFA Images for Single-Sensor Digital Cameras,” IEEE Trans. Image Process. 18(4), 2419–2434 (2009).

Zhang, J.

Zhang, L.

L. Zhang, W. Dong, D. Zhang, and G. Shi, “Two-stage image denoising by principal component analysis with local pixel grouping,” Pattern Recogn. 43(4), 1531–1549 (2010).
[Crossref]

L. Zhang, R. Lukac, X. Wu, and D. Zhang, “PCA-Based Spatially Adaptive Denoising of CFA Images for Single-Sensor Digital Cameras,” IEEE Trans. Image Process. 18(4), 2419–2434 (2009).

Appl. Opt. (2)

Biometrika (1)

D. L. Donoho and I. M. Johnstone, “Ideal spatial adaptation by wavelet shrinkage,” Biometrika,  81(3), 425–455 (1994).
[Crossref]

IEEE Trans. Image Process. (5)

L. Zhang, R. Lukac, X. Wu, and D. Zhang, “PCA-Based Spatially Adaptive Denoising of CFA Images for Single-Sensor Digital Cameras,” IEEE Trans. Image Process. 18(4), 2419–2434 (2009).

S. Chang, B. Yu, and M. Vetterli, “Spatially adaptive wavelet thresholding with context modeling for image denoising,” IEEE Trans. Image Process. 9(9), 1522–1531 (2000).
[Crossref]

M. Elad and M. Aharon, “Image denoising via sparse and redundant representations over learned dictionaries,” IEEE Trans. Image Process. 15(20), 3736–3745 (2006).
[Crossref] [PubMed]

A. Beck and M. Teboulle, “Fast Gradient-Based Algorithms for Constrained Total Variation Image Denoising and Deblurring Problems,” IEEE Trans. Image Process. 18(11), 2419–2434 (2009).
[Crossref] [PubMed]

T. Krishna, C. Creusere, and D. Voelz, “Passive polarimetric imagery-based material classification robust to illumination source position and viewpoint,” IEEE Trans. Image Process. 20(1), 288–292 (2011).
[Crossref]

IEEE Trans. Pattern Anal. Machine Intel. (1)

G. Liu, Z. Lin, S. Yan, J. Sun, Y. Yu, and Y. Ma, “Robust Recovery of Subspace Structures by Low-Rank Representation,” IEEE Trans. Pattern Anal. Machine Intel. 35(1), 171–184 (2013).
[Crossref]

J. Biomed. Opt. (1)

S. Alali and A. Vitkin, “Polarized light imaging in biomedicine: emerging Mueller matrix methodologies for bulk tissue assessment,” J. Biomed. Opt. 20(6), 061104 (2015).
[Crossref]

J. Biophotonics (1)

B. Kunnen, C. Macdonald, A. Doronin, S. Jacques, M. Eccles, and I. Meglinski, “Application of circularly polarized light for non-invasive diagnosis of cancerous tissues and turbid tissue-like scattering media,” J. Biophotonics 8(4), 317–323 (2015).
[Crossref]

J. Opt. (1)

T. Mu, C. Zhang, and R. Liang, “Demonstration of a snapshot full-Stokes division-of-aperture imaging polarimeter using Wollaston prism array,” J. Opt. 17(12), 125708 (2015).
[Crossref]

Opt. Express (9)

S. Gao and V. Gruev, “Gradient-based interpolation method for division of focal plane polarimeters,” Opt. Express 21(1), 1137–1151 (2013).
[Crossref] [PubMed]

J. Zhang, H. Luo, B. Hui, and Z. Chang, “Image interpolation for division of focal plane polarimeters with intensity correlation,” Opt. Express 24(18), 20799–20807 (2016).
[Crossref] [PubMed]

E. Gilboa, J. P. Cunningham, A. Nehorai, and V. Gruev, “Image interpolation and denoising for division of focal plane sensors using Gaussian processes,” Opt. Express 22(12), 15277–15291 (2014).
[Crossref] [PubMed]

G. Myhre, W. Hsu, A. Peinado, C. LaCasse, N. Brock, R. A. Chipman, and S. Pau, “Liquid crystal polymer full-Stokes division of focal plane polarimeter,” Opt. Express 20(25), 27393–27409 (2012).
[Crossref] [PubMed]

S. Fang, X. Xia, X. Huo, and C. Chen, “Image dehazing using polarization effects of objects and airlight,” Opt. Express 22(16),19523–19537 (2014).
[Crossref] [PubMed]

Z. Chen, X. Wang, and R. Liang, “Snapshot phase shift fringe projection 3D surface measurement,” Opt. Express 23(2), 667–673 (2015).
[Crossref] [PubMed]

A. Pierangelo, A. Benali, M. R. Antonelli, T. Novikova, P. Validire, B. Gayet, and A. De Martino, “Ex-vivo characterization of human colon cancer by Mueller polarimetric imaging,” Opt. Express 19(2), 1582–1593 (2011).
[Crossref] [PubMed]

B. Ratliff, C. LaCasse, and S. Tyo, “Interpolation strategies for reducing IFoV artifacts in microgrid polarimeter imagery,” Opt. Express 17(11), 9112–9125 (2009).
[Crossref] [PubMed]

S. Gao and V. Gruev, “Bilinear and bicubic interpolation methods for division of focal plane polarimeters,” Opt. Express 19(27), 26161–26173 (2011).
[Crossref]

Opt. Lett. (1)

Pattern Recogn. (1)

L. Zhang, W. Dong, D. Zhang, and G. Shi, “Two-stage image denoising by principal component analysis with local pixel grouping,” Pattern Recogn. 43(4), 1531–1549 (2010).
[Crossref]

Proc. SPIE (1)

S. Gao and V. Gruev, “Image interpolation methods evaluation for division of focal plane polarimeters,” Proc. SPIE 8012, 80120N (2011).
[Crossref]

Other (1)

Philip R. Bevington and D. Keith Robinson, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, New York, 1992).

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Figures (5)

Fig. 1
Fig. 1 Denoising diagram for DoFP images.
Fig. 2
Fig. 2 Denoising results for simulated DoFP image.
Fig. 3
Fig. 3 PSNR results for different standard variances of noise.
Fig. 4
Fig. 4 RMSE results for different illuminations.
Fig. 5
Fig. 5 Denoising results for real DoFP image.

Equations (16)

Equations on this page are rendered with MathJax. Learn more.

I θ n = I θ + n θ .
x n = [ I 0 ° n I 45 ° n I 135 ° n I 90 ° n ] T = x + n .
s ( x i n , x 0 n ) = exp ( d 2 ( x i n , x 0 n ) 2 σ d 2 x i n x 0 n 2 2 σ r 2 ) .
X n = [ x 0 n , x 1 n , x 2 n , , x M 1 n ] = X + N .
X n ¯ = X n E [ X ] = X E [ X ] + N = X ¯ + N .
C X n ¯ = E [ ( X n ¯ E [ X n ¯ ] ) ( X n ¯ E [ X n ¯ ] ) T ] 1 M X n X n ¯ T = 1 M ( XX ¯ T + X ¯ N T + N X ¯ T + N N T ) .
C X n ¯ = 1 M ( XX ¯ T + NN T ) = C X ¯ + C N .
C X ¯ = QSQ T .
P = Q T .
Y n ¯ = P X n ¯ = P ( X ¯ + N ) = Y ¯ + N y .
Y n ¯ ^ = C Y ¯ C Y n ¯ 1 Y n ¯ .
[ I ^ 0 ° I ^ 45 ° I ^ 135 ° I ^ 90 ° ] = ( P T Y ¯ n ^ + E [ X n ] ) center .
E [ ( I ^ θ I θ n ) ( I ^ θ I θ n ) T ] = E [ ( n r n θ ) ( n r n θ ) T ] = E [ n r n r T ] + E [ n θ n θ T ] E [ n r n θ T ] E [ n θ n r T ] σ θ 2 δ θ 2 .
{ S 0 = I 0 ° + I 90 ° S 1 = I 0 ° I 90 ° S 2 = I 45 ° I 135 ° .
{ σ S 0 = ( ( S 0 ) I 0 ° ) 2 δ 0 ° 2 + ( ( S 0 ) ( I 90 ° ) ) 2 δ 90 ° 2 = δ 0 ° 2 + δ 90 ° 2 σ S 1 = ( S 1 ( I 0 ° ) ) 2 δ 0 ° 2 + ( ( S 1 ) ( I 90 ° ) ) 2 δ 90 ° 2 = δ 0 ° 2 + δ 90 ° 2 σ S 2 = ( ( S 2 ) ( I 45 ° ) ) 2 δ 45 ° 2 + ( ( S 2 ( I 135 ° ) ) 2 δ 135 2 = δ 45 ° 2 + δ 135 ° 2 .
σ = 4 1 H W i = 1 H / 4 j = 1 W / 4 CD 2 ( i , j ) .

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