Abstract

Stripe nonuniformity is very typical in line infrared focal plane arrays (IR-FPA) and uncooled staring IR-FPA. In this paper, the mechanism of the stripe nonuniformity is analyzed, and the gray-scale co- occurrence matrix theory and optimization theory are studied. Through these efforts, the stripe non uniformity correction problem is translated into the optimization problem. The goal of the optimization is to find the minimal energy of the image’s line gradient. After solving the constrained nonlinear opti mization equation, the parameters of the stripe nonuniformity correction are obtained and the stripe nonuniformity correction is achieved. The experiments indicate that this algorithm is effective and efficient.

© 2010 Optical Society of America

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  1. A. F. Milton, F. R. Barone, and M. R. Kruer, “Influence of nonuniformity on infrared focal plane array performance,” Opt. Eng. 24, 855-862 (1985).
  2. D. A. Scribner, M. R. Kruer, and J. M. Killiany, “Infrared focal plane array technology,” Proc. IEEE 79, 66-85 (1991).
    [CrossRef]
  3. J. M. Mooney, F. D. Shepherd, W. S. Ewing, J. E. Murguia, and J. Silverman, “Responsivity nonuniformity limited performance of infrared staring cameras,” Opt. Eng. 28, 1151-1161(1989).
  4. M. Schulz and L. Caldwell, “Nonuniformity correction and correctability of infrared focal plane arrays,” Proc. SPIE 2470, 200-211 (1995).
    [CrossRef]
  5. S. Ullman and G. Schechtman, “Adaptation and gain normalization,” Proc. R. Soc. London Ser. B 216, 299-313(1982).
    [CrossRef]
  6. D. A. Scribner, K. A. Sarkady, J. T. Caulfield, M. R. Kruer, G. Katz, and C. J. Gridly, “Nonuniformity correction for staring IR focal plane arrays using scene-based techniques,” Proc. SPIE 1308, 224-233 (1990).
    [CrossRef]
  7. D. A. Scribner, K. A. Sarkady, and J. T. Caulfield, “Adaptive retina-like preprocessing for imaging detector arrays,” in Proceedings of IEEE International Conference on Neural Networks (IEEE, 1993), Vol. 3, pp. 1955-1960.
    [CrossRef]
  8. J. G. Harris and Y.-M. Chiang, “Nonuniformity correction of infrared image sequences using the constant-statistics constraint,” IEEE Trans. Image Process. 8, 1148-1151 (1999).
    [CrossRef]
  9. H. Shen, T. Ai, and P. Li, “Destriping and inpainting of remote sensing images using maximum a-posteriori method,” in The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences (ISPRS, 2008), Vol. XXXVII, Part B1, pp. 63-70
  10. Z. Yang, J. Li, W. P. Menzel, and R. A. Frey, “De-striping for MODIS data via wavelet shrinkage,” Proc. SPIE 4895, 187-199 (2003).
    [CrossRef]
  11. J. Chen, Y. Shao, H. Guo, W. Wang, and B. Zhu, “Destriping CMODIS data by power filtering,” IEEE Trans. Geosci. Remote Sens. 41, 2119-2114 (2003).
    [CrossRef]
  12. B. K. P. Horn and R. J. Woodham, “Destriping LANDSAT MSS images by histogram modification,” Comput. Graphics Image Process. 10, 69-83 (1979).
    [CrossRef]
  13. J. R. Carr and F. Pellon de Miranda, “The semivariogram in comparison to the co-occurrence matrix for classification of image texture,” IEEE Trans. Geosci. Remote Sens. 36, 1945-1952 (1998).
    [CrossRef]

2003 (2)

Z. Yang, J. Li, W. P. Menzel, and R. A. Frey, “De-striping for MODIS data via wavelet shrinkage,” Proc. SPIE 4895, 187-199 (2003).
[CrossRef]

J. Chen, Y. Shao, H. Guo, W. Wang, and B. Zhu, “Destriping CMODIS data by power filtering,” IEEE Trans. Geosci. Remote Sens. 41, 2119-2114 (2003).
[CrossRef]

1999 (1)

J. G. Harris and Y.-M. Chiang, “Nonuniformity correction of infrared image sequences using the constant-statistics constraint,” IEEE Trans. Image Process. 8, 1148-1151 (1999).
[CrossRef]

1998 (1)

J. R. Carr and F. Pellon de Miranda, “The semivariogram in comparison to the co-occurrence matrix for classification of image texture,” IEEE Trans. Geosci. Remote Sens. 36, 1945-1952 (1998).
[CrossRef]

1995 (1)

M. Schulz and L. Caldwell, “Nonuniformity correction and correctability of infrared focal plane arrays,” Proc. SPIE 2470, 200-211 (1995).
[CrossRef]

1991 (1)

D. A. Scribner, M. R. Kruer, and J. M. Killiany, “Infrared focal plane array technology,” Proc. IEEE 79, 66-85 (1991).
[CrossRef]

1990 (1)

D. A. Scribner, K. A. Sarkady, J. T. Caulfield, M. R. Kruer, G. Katz, and C. J. Gridly, “Nonuniformity correction for staring IR focal plane arrays using scene-based techniques,” Proc. SPIE 1308, 224-233 (1990).
[CrossRef]

1989 (1)

J. M. Mooney, F. D. Shepherd, W. S. Ewing, J. E. Murguia, and J. Silverman, “Responsivity nonuniformity limited performance of infrared staring cameras,” Opt. Eng. 28, 1151-1161(1989).

1985 (1)

A. F. Milton, F. R. Barone, and M. R. Kruer, “Influence of nonuniformity on infrared focal plane array performance,” Opt. Eng. 24, 855-862 (1985).

1982 (1)

S. Ullman and G. Schechtman, “Adaptation and gain normalization,” Proc. R. Soc. London Ser. B 216, 299-313(1982).
[CrossRef]

1979 (1)

B. K. P. Horn and R. J. Woodham, “Destriping LANDSAT MSS images by histogram modification,” Comput. Graphics Image Process. 10, 69-83 (1979).
[CrossRef]

Ai, T.

H. Shen, T. Ai, and P. Li, “Destriping and inpainting of remote sensing images using maximum a-posteriori method,” in The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences (ISPRS, 2008), Vol. XXXVII, Part B1, pp. 63-70

Barone, F. R.

A. F. Milton, F. R. Barone, and M. R. Kruer, “Influence of nonuniformity on infrared focal plane array performance,” Opt. Eng. 24, 855-862 (1985).

Caldwell, L.

M. Schulz and L. Caldwell, “Nonuniformity correction and correctability of infrared focal plane arrays,” Proc. SPIE 2470, 200-211 (1995).
[CrossRef]

Carr, J. R.

J. R. Carr and F. Pellon de Miranda, “The semivariogram in comparison to the co-occurrence matrix for classification of image texture,” IEEE Trans. Geosci. Remote Sens. 36, 1945-1952 (1998).
[CrossRef]

Caulfield, J. T.

D. A. Scribner, K. A. Sarkady, J. T. Caulfield, M. R. Kruer, G. Katz, and C. J. Gridly, “Nonuniformity correction for staring IR focal plane arrays using scene-based techniques,” Proc. SPIE 1308, 224-233 (1990).
[CrossRef]

D. A. Scribner, K. A. Sarkady, and J. T. Caulfield, “Adaptive retina-like preprocessing for imaging detector arrays,” in Proceedings of IEEE International Conference on Neural Networks (IEEE, 1993), Vol. 3, pp. 1955-1960.
[CrossRef]

Chen, J.

J. Chen, Y. Shao, H. Guo, W. Wang, and B. Zhu, “Destriping CMODIS data by power filtering,” IEEE Trans. Geosci. Remote Sens. 41, 2119-2114 (2003).
[CrossRef]

Chiang, Y.-M.

J. G. Harris and Y.-M. Chiang, “Nonuniformity correction of infrared image sequences using the constant-statistics constraint,” IEEE Trans. Image Process. 8, 1148-1151 (1999).
[CrossRef]

Ewing, W. S.

J. M. Mooney, F. D. Shepherd, W. S. Ewing, J. E. Murguia, and J. Silverman, “Responsivity nonuniformity limited performance of infrared staring cameras,” Opt. Eng. 28, 1151-1161(1989).

Frey, R. A.

Z. Yang, J. Li, W. P. Menzel, and R. A. Frey, “De-striping for MODIS data via wavelet shrinkage,” Proc. SPIE 4895, 187-199 (2003).
[CrossRef]

Gridly, C. J.

D. A. Scribner, K. A. Sarkady, J. T. Caulfield, M. R. Kruer, G. Katz, and C. J. Gridly, “Nonuniformity correction for staring IR focal plane arrays using scene-based techniques,” Proc. SPIE 1308, 224-233 (1990).
[CrossRef]

Guo, H.

J. Chen, Y. Shao, H. Guo, W. Wang, and B. Zhu, “Destriping CMODIS data by power filtering,” IEEE Trans. Geosci. Remote Sens. 41, 2119-2114 (2003).
[CrossRef]

Harris, J. G.

J. G. Harris and Y.-M. Chiang, “Nonuniformity correction of infrared image sequences using the constant-statistics constraint,” IEEE Trans. Image Process. 8, 1148-1151 (1999).
[CrossRef]

Horn, B. K. P.

B. K. P. Horn and R. J. Woodham, “Destriping LANDSAT MSS images by histogram modification,” Comput. Graphics Image Process. 10, 69-83 (1979).
[CrossRef]

Katz, G.

D. A. Scribner, K. A. Sarkady, J. T. Caulfield, M. R. Kruer, G. Katz, and C. J. Gridly, “Nonuniformity correction for staring IR focal plane arrays using scene-based techniques,” Proc. SPIE 1308, 224-233 (1990).
[CrossRef]

Killiany, J. M.

D. A. Scribner, M. R. Kruer, and J. M. Killiany, “Infrared focal plane array technology,” Proc. IEEE 79, 66-85 (1991).
[CrossRef]

Kruer, M. R.

D. A. Scribner, M. R. Kruer, and J. M. Killiany, “Infrared focal plane array technology,” Proc. IEEE 79, 66-85 (1991).
[CrossRef]

D. A. Scribner, K. A. Sarkady, J. T. Caulfield, M. R. Kruer, G. Katz, and C. J. Gridly, “Nonuniformity correction for staring IR focal plane arrays using scene-based techniques,” Proc. SPIE 1308, 224-233 (1990).
[CrossRef]

A. F. Milton, F. R. Barone, and M. R. Kruer, “Influence of nonuniformity on infrared focal plane array performance,” Opt. Eng. 24, 855-862 (1985).

Li, J.

Z. Yang, J. Li, W. P. Menzel, and R. A. Frey, “De-striping for MODIS data via wavelet shrinkage,” Proc. SPIE 4895, 187-199 (2003).
[CrossRef]

Li, P.

H. Shen, T. Ai, and P. Li, “Destriping and inpainting of remote sensing images using maximum a-posteriori method,” in The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences (ISPRS, 2008), Vol. XXXVII, Part B1, pp. 63-70

Menzel, W. P.

Z. Yang, J. Li, W. P. Menzel, and R. A. Frey, “De-striping for MODIS data via wavelet shrinkage,” Proc. SPIE 4895, 187-199 (2003).
[CrossRef]

Milton, A. F.

A. F. Milton, F. R. Barone, and M. R. Kruer, “Influence of nonuniformity on infrared focal plane array performance,” Opt. Eng. 24, 855-862 (1985).

Mooney, J. M.

J. M. Mooney, F. D. Shepherd, W. S. Ewing, J. E. Murguia, and J. Silverman, “Responsivity nonuniformity limited performance of infrared staring cameras,” Opt. Eng. 28, 1151-1161(1989).

Murguia, J. E.

J. M. Mooney, F. D. Shepherd, W. S. Ewing, J. E. Murguia, and J. Silverman, “Responsivity nonuniformity limited performance of infrared staring cameras,” Opt. Eng. 28, 1151-1161(1989).

Pellon de Miranda, F.

J. R. Carr and F. Pellon de Miranda, “The semivariogram in comparison to the co-occurrence matrix for classification of image texture,” IEEE Trans. Geosci. Remote Sens. 36, 1945-1952 (1998).
[CrossRef]

Sarkady, K. A.

D. A. Scribner, K. A. Sarkady, J. T. Caulfield, M. R. Kruer, G. Katz, and C. J. Gridly, “Nonuniformity correction for staring IR focal plane arrays using scene-based techniques,” Proc. SPIE 1308, 224-233 (1990).
[CrossRef]

D. A. Scribner, K. A. Sarkady, and J. T. Caulfield, “Adaptive retina-like preprocessing for imaging detector arrays,” in Proceedings of IEEE International Conference on Neural Networks (IEEE, 1993), Vol. 3, pp. 1955-1960.
[CrossRef]

Schechtman, G.

S. Ullman and G. Schechtman, “Adaptation and gain normalization,” Proc. R. Soc. London Ser. B 216, 299-313(1982).
[CrossRef]

Schulz, M.

M. Schulz and L. Caldwell, “Nonuniformity correction and correctability of infrared focal plane arrays,” Proc. SPIE 2470, 200-211 (1995).
[CrossRef]

Scribner, D. A.

D. A. Scribner, M. R. Kruer, and J. M. Killiany, “Infrared focal plane array technology,” Proc. IEEE 79, 66-85 (1991).
[CrossRef]

D. A. Scribner, K. A. Sarkady, J. T. Caulfield, M. R. Kruer, G. Katz, and C. J. Gridly, “Nonuniformity correction for staring IR focal plane arrays using scene-based techniques,” Proc. SPIE 1308, 224-233 (1990).
[CrossRef]

D. A. Scribner, K. A. Sarkady, and J. T. Caulfield, “Adaptive retina-like preprocessing for imaging detector arrays,” in Proceedings of IEEE International Conference on Neural Networks (IEEE, 1993), Vol. 3, pp. 1955-1960.
[CrossRef]

Shao, Y.

J. Chen, Y. Shao, H. Guo, W. Wang, and B. Zhu, “Destriping CMODIS data by power filtering,” IEEE Trans. Geosci. Remote Sens. 41, 2119-2114 (2003).
[CrossRef]

Shen, H.

H. Shen, T. Ai, and P. Li, “Destriping and inpainting of remote sensing images using maximum a-posteriori method,” in The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences (ISPRS, 2008), Vol. XXXVII, Part B1, pp. 63-70

Shepherd, F. D.

J. M. Mooney, F. D. Shepherd, W. S. Ewing, J. E. Murguia, and J. Silverman, “Responsivity nonuniformity limited performance of infrared staring cameras,” Opt. Eng. 28, 1151-1161(1989).

Silverman, J.

J. M. Mooney, F. D. Shepherd, W. S. Ewing, J. E. Murguia, and J. Silverman, “Responsivity nonuniformity limited performance of infrared staring cameras,” Opt. Eng. 28, 1151-1161(1989).

Ullman, S.

S. Ullman and G. Schechtman, “Adaptation and gain normalization,” Proc. R. Soc. London Ser. B 216, 299-313(1982).
[CrossRef]

Wang, W.

J. Chen, Y. Shao, H. Guo, W. Wang, and B. Zhu, “Destriping CMODIS data by power filtering,” IEEE Trans. Geosci. Remote Sens. 41, 2119-2114 (2003).
[CrossRef]

Woodham, R. J.

B. K. P. Horn and R. J. Woodham, “Destriping LANDSAT MSS images by histogram modification,” Comput. Graphics Image Process. 10, 69-83 (1979).
[CrossRef]

Yang, Z.

Z. Yang, J. Li, W. P. Menzel, and R. A. Frey, “De-striping for MODIS data via wavelet shrinkage,” Proc. SPIE 4895, 187-199 (2003).
[CrossRef]

Zhu, B.

J. Chen, Y. Shao, H. Guo, W. Wang, and B. Zhu, “Destriping CMODIS data by power filtering,” IEEE Trans. Geosci. Remote Sens. 41, 2119-2114 (2003).
[CrossRef]

Comput. Graphics Image Process. (1)

B. K. P. Horn and R. J. Woodham, “Destriping LANDSAT MSS images by histogram modification,” Comput. Graphics Image Process. 10, 69-83 (1979).
[CrossRef]

IEEE Trans. Geosci. Remote Sens. (2)

J. R. Carr and F. Pellon de Miranda, “The semivariogram in comparison to the co-occurrence matrix for classification of image texture,” IEEE Trans. Geosci. Remote Sens. 36, 1945-1952 (1998).
[CrossRef]

J. Chen, Y. Shao, H. Guo, W. Wang, and B. Zhu, “Destriping CMODIS data by power filtering,” IEEE Trans. Geosci. Remote Sens. 41, 2119-2114 (2003).
[CrossRef]

IEEE Trans. Image Process. (1)

J. G. Harris and Y.-M. Chiang, “Nonuniformity correction of infrared image sequences using the constant-statistics constraint,” IEEE Trans. Image Process. 8, 1148-1151 (1999).
[CrossRef]

Opt. Eng. (2)

A. F. Milton, F. R. Barone, and M. R. Kruer, “Influence of nonuniformity on infrared focal plane array performance,” Opt. Eng. 24, 855-862 (1985).

J. M. Mooney, F. D. Shepherd, W. S. Ewing, J. E. Murguia, and J. Silverman, “Responsivity nonuniformity limited performance of infrared staring cameras,” Opt. Eng. 28, 1151-1161(1989).

Proc. IEEE (1)

D. A. Scribner, M. R. Kruer, and J. M. Killiany, “Infrared focal plane array technology,” Proc. IEEE 79, 66-85 (1991).
[CrossRef]

Proc. R. Soc. London Ser. B (1)

S. Ullman and G. Schechtman, “Adaptation and gain normalization,” Proc. R. Soc. London Ser. B 216, 299-313(1982).
[CrossRef]

Proc. SPIE (3)

D. A. Scribner, K. A. Sarkady, J. T. Caulfield, M. R. Kruer, G. Katz, and C. J. Gridly, “Nonuniformity correction for staring IR focal plane arrays using scene-based techniques,” Proc. SPIE 1308, 224-233 (1990).
[CrossRef]

M. Schulz and L. Caldwell, “Nonuniformity correction and correctability of infrared focal plane arrays,” Proc. SPIE 2470, 200-211 (1995).
[CrossRef]

Z. Yang, J. Li, W. P. Menzel, and R. A. Frey, “De-striping for MODIS data via wavelet shrinkage,” Proc. SPIE 4895, 187-199 (2003).
[CrossRef]

Other (2)

D. A. Scribner, K. A. Sarkady, and J. T. Caulfield, “Adaptive retina-like preprocessing for imaging detector arrays,” in Proceedings of IEEE International Conference on Neural Networks (IEEE, 1993), Vol. 3, pp. 1955-1960.
[CrossRef]

H. Shen, T. Ai, and P. Li, “Destriping and inpainting of remote sensing images using maximum a-posteriori method,” in The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences (ISPRS, 2008), Vol. XXXVII, Part B1, pp. 63-70

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Figures (11)

Fig. 1
Fig. 1

Image of the uncooled staring IR-FPA; it has the column stripe nonuniformity.

Fig. 2
Fig. 2

(a) Image without stripe nonuniformity. (b) The gray-scale co-occurrence matrix of this image.

Fig. 3
Fig. 3

(a) Edge area and non-edge area of the image without stripe nonuniformity (white means edge area and black means non-edge area). (b) The non-edge-area gray-scale co-occurrence matrix of this image.

Fig. 4
Fig. 4

(a) Image added with the stripe nonuniformity. (b) The edge area and non-edge area of the image with stripe nonuniformity (white means edge area and black means non-edge area). (c) The non-edge-area gray-scale co-occurrence matrix of the image with stripe nonuniformity.

Fig. 5
Fig. 5

(a), (c), (e) Origin images; (b), (d), (f) are the stripe NUC image.

Fig. 6
Fig. 6

(a) Non-edge-area gray-scale co-occurrence matrix of Fig. 5e. (b) The non-edge-area gray-scale co-occurrence matrix of Fig. 5f.

Fig. 7
Fig. 7

(a) Uniform image whose gray value equals to 128. (b) The uniform image added with the stripe nonuniformity and pixel nonuniformity (pixel nonuniformity’s variance equals 4, and the variance of the stripe nonuniformity’s offset β j ( T B , t ) equals 2). (c) The image after stripe NUC.

Fig. 8
Fig. 8

(a) Curves of E 1 , E 2 , E 3 from Table 2. (b) The curves of E 1 , E 2 , E 3 from Table 3.

Fig. 9
Fig. 9

(a) Original image with stripe nonuniformity. (b) The edge area and non-edge area of the image with stripe nonuniformity (white means edge area and black means non-edge area). (c) The stripe NUC processed image.

Fig. 10
Fig. 10

Original image with stripe nonuniformity and Gaussian noise (Gaussian noise mean equals to 0 and variance equals to 15).

Fig. 11
Fig. 11

(a) Power filtering destriping algorithm processed image of Fig. 5e. (b) The power filtering destriping algorithm processed image of Fig. 9a.

Tables (5)

Tables Icon

Table 1 Comparison of the Energy of Line Gradient E between the Original Images in Figs. 5a, 5c, 5e and the Stripe Nonuniformity Correction Images in Figs. 5b, 5d, 5f

Tables Icon

Table 2 Comparison of the Energy of Line Gradient E on Different Pixel Nonuniformity Variance a

Tables Icon

Table 3 Comparison of the Energy of Line Gradient E on Different Pixel Nonuniformity Variance a

Tables Icon

Table 4 Comparison of Mean-Square Error and Peak Signal-to-Noise Ratio before and after Nonuniformity Correction

Tables Icon

Table 5 Comparison of Mean-Square Error and Peak Signal-to-Noise Ratio before and after Nonuniformity Correction

Equations (20)

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

V = F ( X , T B ) .
V F ( X 0 , T B 0 ) + F ( X 0 , T B 0 ) X ( X X 0 ) + F ( X 0 , T B 0 ) T B ( T B T B 0 ) .
V out = α V + β = α F ( X 0 , T B 0 ) + α F ( X 0 , T B 0 ) X ( X X 0 ) + α F ( X 0 , T B 0 ) T B ( T B T B 0 ) + β .
V out ( i , j ) = α j F i , j ( X 0 , T B 0 ) + α j F i , j ( X 0 , T B 0 ) X ( X X 0 ) + α j F i , j ( X 0 , T B 0 ) T B ( T B T B 0 ) + β j ,
V out 0 ( i , j ) = α j F i , j ( X 0 , T B 0 ) + β j ,
V out ( i , j ) = V out V out 0 = α j F i , j ( X 0 , T B 0 ) X ( X X 0 ) + α j F i , j ( X 0 , T B 0 ) T B ( T B T B 0 ) .
V out ( i , j ) = α j ( T B ) F i , j ( X 0 , T B 0 ) + α j ( T B ) F i , j ( X 0 , T B 0 ) X ( X X 0 ) + α j ( T B ) F i , j ( X 0 , T B 0 ) T B ( T B T B 0 ) + β j ( T B , t ) .
V out ( i , j ) = α j ( T B ) [ F i , j ( X 0 , T B 0 ) X ( X X 0 ) + F i , j ( X 0 , T B 0 ) T B ( T B T B 0 ) ] + β j ( T B , t ) , β j ( T B , t ) = β j ( T B , t ) β j ( T B 0 , t 0 ) .
V out ( i , j ) = [ V out ( i , j ) β j ( T B , t ) ] / α j ( T B ) = F i , j ( X 0 , T B 0 ) X ( X X 0 ) + F i , j ( X 0 , T B 0 ) T B ( T B T B 0 ) .
H 2 D ( p , q ) = i j { 1 if     G 1 = p and G 2 = q 0 else where     G 1 = I i , j , G 2 = I i , j 1 .
T i ( j , j 1 ) = { 1 | I i , j I i , j 1 | Th edge 0 else .
E = 1 Ω j i ( I i , j I i , j 1 ) T i ( j , j 1 ) ( i = 1 , ... , N , j = 1 , ... , M ) where     Ω = j = 2 M i = 1 N T i ( j , j 1 ) .
E = 1 Ω j i ( P i , j P i , j 1 ) T i ( j , j 1 ) ( i = 1 , ... , N , j = 1 , ... , M ) where     P i , j = a j I i , j + b j , a j = 1 / α j ( T B ) , b j = β j ( T B , t ) / α j ( T B ) .
1 M × N i j P i , j I i , j Th diff ( i = 1 , ... , N , j = 1 , ... , M ) .
min J = 1 Ω j i ( a j I i , j + b j a j 1 I i , j 1 b j 1 ) T i ( j , j 1 ) ( i = 1 , ... , N , j = 1 , ... , M ) , s u b j e c t t o     1 M × N i j a j I i , j + b j I i , j Th diff .
MSE = i = 1 N j = 1 M ( I n P n ) 2 M × N ,
PSNR = 10 × log ( 255 2 MSE ) .
MSE ( b NUC ) = i = 1 N j = 1 M [ I n P n ( b NUC ) ] 2 M × N ,
MSE ( a NUC ) = i = 1 N j = 1 M [ I n P n ( a NUC ) ] 2 M × N .
min J j = i ( a j I i , j b j a j 1 I i , j 1 + b j 1 ) T i ( j , j 1 ) + i ( a j 1 I i , j 1 + b j 1 a j 2 I i , j 2 b j 2 ) T i ( j , j 2 ) ( i = 1 , ... , N , j = 3 , ... , M ) s u b j e c t t o     1 3 × N i l = j 2 j a l I i , l + b l I i , l Th diff .

Metrics