Abstract

Detection of defective pixels in solid-state detectors/sensor arrays has received limited research attention. Few approaches currently exist for detecting the defective pixels using real images captured with cameras equipped with such detectors, and they are ad hoc and limited in their applicability. In this paper, we present a probabilistic novel integrated technique for autonomously detecting the defective pixels in image sensor arrays. It can be applied to images containing rich scene information, captured with any digital camera equipped with a solid-state detector, to detect different kinds of defective pixels in the detector. We apply our technique to the detection of various defective pixels in an experimental camera equipped with a charge coupled device (CCD) array and two out of the four HgCdTe detectors of the UKIRT’s wide field camera (WFCAM) used for infrared (IR) astronomy [Astron. Astrophys. 467, 777–784 (2007)].

© 2008 Optical Society of America

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2008

S. Ghosh, I. Marshall, and A. Freitas, “Autonomously detecting the defective pixels in an imaging sensor array using a robust statistical technique,” Proc. SPIE 6808, 680813(2008).

2007

M. Casali, A. Adamson, C. Alves de Oliveira, O. Almaini, K. Burch, T. Chuter, J. Elliot, M. Folger, S. Foucaud, N. Hambly, M. Hastie, D. Henry, P. Hirst, M. Irwin, D. Ives, A. Lawrence, K. Laidlaw, D. Lee, J. Lewis, D. Lunney, S. McLay, D. Montgomery, A. Pickup, M. Read, N. Rees, I. Robson, K. Sekiguchi, A. Vick, S. Warren, and B. Woodward, “The UKIRT wide-field camera,” Astron. Astrophys. 467, 777-784 (2007).

G. H. Rieke, “Infrared detector arrays for astronomy,” Annu. Rev. Astron. Astrophys. 45, 77-115 (2007).
[CrossRef]

E. Courses and T. Surveys, “Influence of terrestrial cosmic rays on the reliability of CCD image sensors--Part 1: Experiments at room temperature,” IEEE Trans. Electron Devices 54, 3260-3266 (2007).

A. Lawrence, S. J. Warren, O. Almaini, A. C. Edge, N. C. Hambly, R. F. Jameson, P. Lucas, M. Casali, A. Adamson, S. Dye, J. P. Emerson, S. Foucaud, P. Hewett, P. Hirst, S. T. Hodgkin, M. J. Irwin, N. Lodieu, R. G. McMahon, C. Simpson, I. Smail, D. Mortlock, and M. Folger, “The UKIRT Infrared Deep Sky Survey (UKIDSS),” Mon. Not. R. Astron. Soc. 379, 1599-1617 (2007).
[CrossRef]

C. Archambeau and M. Verleysen, “Robust Bayesian clustering,” Neural Netw. 20, 129-138 (2007).
[CrossRef]

2006

T. Fawcett, “An introduction to ROC analysis,” Pattern Recogn. Lett. 27, 861-874 (2006).
[CrossRef]

J. Dudas, C. Jung, G. Chapman, Z. Koren, and I. Koren, “Robust detection of defects in imaging arrays,” Proc. SPIE 6059, 60590X (2006).
[CrossRef]

D. Odom and P. Milanfar, “Modeling multiscale differential pixel statistics,” Proc. SPIE 6065, 16-24 (2006).

2005

A. Buades, B. Coll, and J. Morel, “A review of image denoising algorithms, with a new one,” Multiscale Model. Simul. 4, 490-530 (2005).

M. Svensén and C. Bishop, “Robust Bayesian mixture modelling,” Neurocomputing 64, 235-252 (2005).
[CrossRef]

2004

M. Irwin, J. Lewis, S. Hodgkin, P. Bunclark, D. Evans, R. McMahon, J. Emerson, M. Stewart, and S. Beard, “VISTA data flow system: pipeline processing for WFCAM and VISTA,” Proc. SPIE 5493, 411-422 (2004).
[CrossRef]

Z. Zivkovic and F. van der Heijden, “Recursive unsupervised learning of finite mixture models,” IEEE Trans. Pattern Anal. Mach. Intell. 26, 651-656 (2004).

2003

D. Froebrich and A. Scholz, “Young stars and outflows in the globule IC 1396 W,” Astron. Astrophys. 407, 207-212(2003).

S. Riffat and X. Ma, “Thermoelectrics: a review of present and potential applications,” Appl. Th. Eng. 23, 913-935 (2003).
[CrossRef]

C. Biernacki, G. Celeux, and G. Govaert, “Choosing starting values for the EM algorithm for getting the highest likelihood in multivariate Gaussian mixture models,” Comput. Stat. Data Anal. 41, 561-575 (2003).
[CrossRef]

B. Jin, N. George, and K. Yeary, “Modeling and analysis of soft-test/repair for CCD-based digital x-ray systems,” IEEE Trans. Instrum. Meas. 52, 1713-1721 (2003).

2002

A. Rogalski, “Infrared detectors: an overview,” Infrared Phys. Technol. 43, 187-210 (2002).

J. M. Lopez-Alonso and J. Alda, “Bad pixel identification by means of principal components analysis,” Opt. Eng. 41, 2152-2157 (2002).

M. A. T. Figueiredo and A. K. Jain, “Unsupervised learning of finite mixture models,” IEEE Trans. Pattern Anal. Mach. Intell. 24, 381-396 (2002).

2000

C. Biernacki, G. Celeux, and G. Govaert, “Assessing a mixture model for clustering with the integrated completed likelihood,” IEEE Trans. Pattern Anal. Mach. Intell. 22, 719-725(2000).
[CrossRef]

D. Peel and G. McLachlan, “Robust mixture modelling using the t distribution,” Stat. Comput. 10, 339-348 (2000).
[CrossRef]

1999

G. Min and D. Rowe, “Cooling performance of integrated thermoelectric microcooler,” Solid-State Electron. 43, 923-929(1999).

1998

C. Fraley and A. E. Raftery, “How many clusters? Which clustering method? Answers via model-based cluster analysis,” Comput. J. 41, 578-588 (1998).

1997

P. Domingos and M. Pazzani, “On the optimality of the simple Bayesian classifier under zero-one loss,” Mach. Learn. 29, 103-130 (1997).
[CrossRef]

K. Roeder and L. Wasserman, “Practical Bayesian density estimation using mixtures of norms,” J. Am. Stat. Assoc. 92(1997).

A. Bradley, “The use of the area under the ROC curve in the evaluation of machine learning algorithms,” Pattern Recogn. 30, 1145-1159 (1997).
[CrossRef]

1996

E. Bertin and S. Arnouts, “Sextractor: Software for source extraction,” Astron. Astrophys. Suppl. Ser. 117, 393-404(1996).
[CrossRef]

L. Xu and M. Jordan, “On convergence properties of the EM algorithm for Gaussian mixtures,” Neural Comput. 8, 129-151(1996).
[CrossRef]

1995

J. Brailean, R. Kleihorst, S. Efstratiadis, A. Katsaggelos, and R. Lagendijk, “Noise reduction filters for dynamic image sequences: a review,” Proc. IEEE 83, 1272-1292 (1995).
[CrossRef]

1994

R. Rogers and A. Riess, “Detection and classification of CCD defects with an artificial neural network,” Publ. Astron. Soc. Pac. 106, 532-541 (1994).

1988

J. A. Swets, “Measuring the accuracy of diagnostic systems,” Science 240, 1285-1293 (1988).
[CrossRef]

1986

C. D. Mackay, “Charge-coupled devices in astronomy,” Annu. Rev. Astron. Astrophys. 24, 255-283 (1986).
[CrossRef]

1984

R. Redner and H. Walker, “Mixture densities, maximum likelihood and the em algorithm,” SIAM Rev. 26, 195-239(1984).
[CrossRef]

1977

A. P. Dempster, N. M. Laird, and D. B. Rubin, “Maximum likelihood from incomplete data via the em algorithm,” J. R. Stat. Soc. Ser. B Methodol. 39, 1-38 (1977).

1972

P. Huber, “Robust statistics: a review,” Ann. Stat. 43, 1041-1061 (1972).

1965

P. Bickel, “On some robust estimates of location,” Ann. Math. Stat. 36, 847-858 (1965).

Acharya, T.

T. Yap-Peng and T. Acharya, “A robust sequential approach for the detection of defective pixels in an image sensor,” in Proceeding of IEEE International Conference On Acoustics, Speech, and Signal Processing (ICASSP 99) (IEEE, 1999), pp. 2239-2242.

Adamson, A.

A. Lawrence, S. J. Warren, O. Almaini, A. C. Edge, N. C. Hambly, R. F. Jameson, P. Lucas, M. Casali, A. Adamson, S. Dye, J. P. Emerson, S. Foucaud, P. Hewett, P. Hirst, S. T. Hodgkin, M. J. Irwin, N. Lodieu, R. G. McMahon, C. Simpson, I. Smail, D. Mortlock, and M. Folger, “The UKIRT Infrared Deep Sky Survey (UKIDSS),” Mon. Not. R. Astron. Soc. 379, 1599-1617 (2007).
[CrossRef]

M. Casali, A. Adamson, C. Alves de Oliveira, O. Almaini, K. Burch, T. Chuter, J. Elliot, M. Folger, S. Foucaud, N. Hambly, M. Hastie, D. Henry, P. Hirst, M. Irwin, D. Ives, A. Lawrence, K. Laidlaw, D. Lee, J. Lewis, D. Lunney, S. McLay, D. Montgomery, A. Pickup, M. Read, N. Rees, I. Robson, K. Sekiguchi, A. Vick, S. Warren, and B. Woodward, “The UKIRT wide-field camera,” Astron. Astrophys. 467, 777-784 (2007).

Alda, J.

J. M. Lopez-Alonso and J. Alda, “Bad pixel identification by means of principal components analysis,” Opt. Eng. 41, 2152-2157 (2002).

Aldcroft, T. L.

M. Cresitello-Dittmar, T. L. Aldcroft, and D. Morris, “On the fly bad pixel detection for the chandra x-ray observatory's aspect camera,” in Astronomical Data Analysis Software and Systems X, vol. 238, (Astronomical Society of the Pacific, 2001).

Almaini, O.

A. Lawrence, S. J. Warren, O. Almaini, A. C. Edge, N. C. Hambly, R. F. Jameson, P. Lucas, M. Casali, A. Adamson, S. Dye, J. P. Emerson, S. Foucaud, P. Hewett, P. Hirst, S. T. Hodgkin, M. J. Irwin, N. Lodieu, R. G. McMahon, C. Simpson, I. Smail, D. Mortlock, and M. Folger, “The UKIRT Infrared Deep Sky Survey (UKIDSS),” Mon. Not. R. Astron. Soc. 379, 1599-1617 (2007).
[CrossRef]

M. Casali, A. Adamson, C. Alves de Oliveira, O. Almaini, K. Burch, T. Chuter, J. Elliot, M. Folger, S. Foucaud, N. Hambly, M. Hastie, D. Henry, P. Hirst, M. Irwin, D. Ives, A. Lawrence, K. Laidlaw, D. Lee, J. Lewis, D. Lunney, S. McLay, D. Montgomery, A. Pickup, M. Read, N. Rees, I. Robson, K. Sekiguchi, A. Vick, S. Warren, and B. Woodward, “The UKIRT wide-field camera,” Astron. Astrophys. 467, 777-784 (2007).

Archambeau, C.

C. Archambeau and M. Verleysen, “Robust Bayesian clustering,” Neural Netw. 20, 129-138 (2007).
[CrossRef]

Arnouts, S.

E. Bertin and S. Arnouts, “Sextractor: Software for source extraction,” Astron. Astrophys. Suppl. Ser. 117, 393-404(1996).
[CrossRef]

Audet, Y.

G. Chapman and Y. Audet, “Creating 35 mm camera active pixel sensors,” in Proceedings on the 14th International Symposium on Defect and Fault-Tolerance in VLSI Systems (DFT 99) (IEEE, 1999), pp. 22-30.

Banerjee, A.

V. Chandola, A. Banerjee, and V. Kumar, “Outlier detection: a survey,” Tech. rep. (University of Minnesota, 2007).

Barnett, V.

V. Barnett and T. Lewis, Outliers in Statistical Data, 3rd ed. (Wiley, 1994).

Basford, K.

G. McLachlan and K. Basford, Mixture Models. Inference and Applications to Clustering (M. Dekker, 1988).

Beard, S.

M. Irwin, J. Lewis, S. Hodgkin, P. Bunclark, D. Evans, R. McMahon, J. Emerson, M. Stewart, and S. Beard, “VISTA data flow system: pipeline processing for WFCAM and VISTA,” Proc. SPIE 5493, 411-422 (2004).
[CrossRef]

Bertin, E.

E. Bertin and S. Arnouts, “Sextractor: Software for source extraction,” Astron. Astrophys. Suppl. Ser. 117, 393-404(1996).
[CrossRef]

Bickel, P.

P. Bickel, “On some robust estimates of location,” Ann. Math. Stat. 36, 847-858 (1965).

Biernacki, C.

C. Biernacki, G. Celeux, and G. Govaert, “Choosing starting values for the EM algorithm for getting the highest likelihood in multivariate Gaussian mixture models,” Comput. Stat. Data Anal. 41, 561-575 (2003).
[CrossRef]

C. Biernacki, G. Celeux, and G. Govaert, “Assessing a mixture model for clustering with the integrated completed likelihood,” IEEE Trans. Pattern Anal. Mach. Intell. 22, 719-725(2000).
[CrossRef]

Bishop, C.

M. Svensén and C. Bishop, “Robust Bayesian mixture modelling,” Neurocomputing 64, 235-252 (2005).
[CrossRef]

Bradley, A.

A. Bradley, “The use of the area under the ROC curve in the evaluation of machine learning algorithms,” Pattern Recogn. 30, 1145-1159 (1997).
[CrossRef]

Brailean, J.

J. Brailean, R. Kleihorst, S. Efstratiadis, A. Katsaggelos, and R. Lagendijk, “Noise reduction filters for dynamic image sequences: a review,” Proc. IEEE 83, 1272-1292 (1995).
[CrossRef]

Buades, A.

A. Buades, B. Coll, and J. Morel, “A review of image denoising algorithms, with a new one,” Multiscale Model. Simul. 4, 490-530 (2005).

Bunclark, P.

M. Irwin, J. Lewis, S. Hodgkin, P. Bunclark, D. Evans, R. McMahon, J. Emerson, M. Stewart, and S. Beard, “VISTA data flow system: pipeline processing for WFCAM and VISTA,” Proc. SPIE 5493, 411-422 (2004).
[CrossRef]

Burch, K.

M. Casali, A. Adamson, C. Alves de Oliveira, O. Almaini, K. Burch, T. Chuter, J. Elliot, M. Folger, S. Foucaud, N. Hambly, M. Hastie, D. Henry, P. Hirst, M. Irwin, D. Ives, A. Lawrence, K. Laidlaw, D. Lee, J. Lewis, D. Lunney, S. McLay, D. Montgomery, A. Pickup, M. Read, N. Rees, I. Robson, K. Sekiguchi, A. Vick, S. Warren, and B. Woodward, “The UKIRT wide-field camera,” Astron. Astrophys. 467, 777-784 (2007).

Casali, M.

M. Casali, A. Adamson, C. Alves de Oliveira, O. Almaini, K. Burch, T. Chuter, J. Elliot, M. Folger, S. Foucaud, N. Hambly, M. Hastie, D. Henry, P. Hirst, M. Irwin, D. Ives, A. Lawrence, K. Laidlaw, D. Lee, J. Lewis, D. Lunney, S. McLay, D. Montgomery, A. Pickup, M. Read, N. Rees, I. Robson, K. Sekiguchi, A. Vick, S. Warren, and B. Woodward, “The UKIRT wide-field camera,” Astron. Astrophys. 467, 777-784 (2007).

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Figures (12)

Fig. 1
Fig. 1

Examples of defining a block of pixels for integrated technique.

Fig. 2
Fig. 2

Methodology of integration for d = 1 .

Fig. 3
Fig. 3

Histograms of (a) and (c) two different samples of PSDEs and (b) and (d)  the corresponding estimated GMMs.

Fig. 4
Fig. 4

Independence of the inputs in δ i , given a class C k .

Fig. 5
Fig. 5

Identifying the faulty pixels based on the ranking in terms of proportions of classification in the ‘High’ component.

Fig. 6
Fig. 6

Camera setup showing the camera attached to calibration cooler and thermostat.

Fig. 7
Fig. 7

Experimental setup showing the camera, light source, and optical diffuser plates mounted on an optical rail.

Fig. 8
Fig. 8

Sample images captured with experimental camera.

Fig. 9
Fig. 9

Four detector arrays on WFCAM.

Fig. 10
Fig. 10

ROC curves for Detector 1 and 4 for different thresholds (th).

Fig. 11
Fig. 11

Coadded images with no mask showing (a) defective pixels, (b) removal of defective pixels in with UKIRT’s mask, and (c) our mask.

Fig. 12
Fig. 12

Comparison of stellar photometry.

Tables (9)

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Table 1 Posterior Probabilities and Classification of Pairwise Difference Estimates

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Table 2 Detection Rate for Different Numbers of Image Data Sets

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Table 3 Numbers of Selections of Different Numbers of GMM Components by the BIC Criterion (K) in 30 Trials

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Table 4 Effect of Number of Images on Performance a

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Table 5 Effect of Number of Pixels on Performance a

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Table 6 Effect of Parameter p on Detection Rate a

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Table 7 Performance at the Detection of Different Faulty Pixels Detected by the Ground-Truth Technique a

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Table 8 Performance of our Technique at Detecting Different Pixels Subject to Different Values of Gain (m) a

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Table 9 Performance of our Technique at Detecting Clusters of Defective Pixels, Subject to Different Values of Gain (m) a

Equations (10)

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

M i j = M i j mean ( M j ) std ( M j ) , where     i = 1 , , n and j = 1 , , p .
Δ a b = j = 1 p | M a j M b j | .
P k ( Δ i | θ k ) = 1 σ k 2 π e ( Δ i μ k ) 2 / 2 σ k 2 .
L ( θ k , π k , z i k | Δ i ) = i = 1 ( n 2 n ) × d / 2 k = 1 K z i k [ log π k P ( Δ i | θ k ) ] .
P ( C k | δ i ) = P ( C k ) × P ( δ i | C k ) k = 1 K P ( C k ) × P ( δ i | C k ) .
classify ( δ i ) = arg max P ( C k | δ i ) k .
P ( C k | δ i ) = P ( C k ) × j = d + 1 N P ( Δ i j | C k ) k = 1 K P ( C k ) × j = d + 1 N P ( Δ i j | C k ) .
P ( C k | δ i ) = α k × j = d + 1 N P ( Δ i j | μ k , σ k ) k = 1 K α k × j = d + 1 N P ( Δ i j | μ k , σ k ) .
Z i = M i c μ c σ where     i = 1 , , n .
TPR = TP TP + FN FPR = FP FP + TN .

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