Abstract

Several imaging devices are characterized by a space-variant point-spread function (PSF), such as the wide-field/planetary camera of the Hubble Space Telescope (HST). Several techniques for image recovery that use data from such imagers approximate the space-variant PSF by a space-invariant PSF. A modified Richardson-Lucy method is implemented that accommodates the space-variant PSF of the HST as well as corrections for background counts, nonuniform flat field, and readout noise. The implementation runs on the DEC mppl2000 Sx/Model 200 massively parallel computer. Restorations of simulated HST images are obtained with a space-variant PSF and, for comparison, with a space-invariant approximation. Results of these processing methods are compared, and it is found that a residual artifact appears in restorations when a space-invariant PSF is used owing to the mismatch of the PSF kernel used in the restoration and the space-variant one underlying the image acquired with the telescope. This residual artifact is effectively eliminated when the processing is based on the space-variant PSF.

© 1995 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. R. L. White, R. J. Allen, eds., Proceedings of Workshop: The Restoration of HST Images and Spectra (Space Telescope Science Institute, Baltimore, Md., 1990).
  2. R. J. Hanish, R. L. White, eds., Proceedings of Workshop: The Restoration of HST Images and Spectra II (Space Telescope Science Institute, Baltimore, Md., 1993).
  3. R. J. Hanisch, “Linear restoration techniques: not all bad,” in Proceedings of Workshop: The Restoration of HST Images and Spectra, R. L. White, R. J. Allen, eds. (Space Telescope Science Institute, Baltimore, Md., 1990), pp. 127–131.
  4. D. L. Snyder, A. M. Hammoud, R. L. White, “Image recovery from data acquired with a charge-coupled-device camera,” J. Opt. Soc. Am. A 10, 1014–1023 (1993).
    [Crossref] [PubMed]
  5. D. L. Snyder, C. W. Helstrom, A. D. Lanterman, M. Faisal, R. L. White, “Compensation for read-out noise in charge-coupled-device images,” J. Opt. Soc. Am. A 12, 272–283 (1995).
    [Crossref]
  6. D. L. Snyder, T. J. Schulz, J. A. O’Sullivan, “Deblurring subject to nonnegativity constraints,” IEEE Trans. Signal Process. 40, 1143–1150 (1992).
    [Crossref]
  7. MasPar MP-1 Architecture Specification, MasPar MP-1 System Hardware Manual (MasPar Computer Corporation, Sunnyvale, Calif., 1991), p. 1.2.
  8. J. Krist, The Tiny Tim User’s Manual, V. 4.0 (Space Telescope Science Institute, Baltimore, Md., 1994).

1995 (1)

1993 (1)

1992 (1)

D. L. Snyder, T. J. Schulz, J. A. O’Sullivan, “Deblurring subject to nonnegativity constraints,” IEEE Trans. Signal Process. 40, 1143–1150 (1992).
[Crossref]

Faisal, M.

Hammoud, A. M.

Hanisch, R. J.

R. J. Hanisch, “Linear restoration techniques: not all bad,” in Proceedings of Workshop: The Restoration of HST Images and Spectra, R. L. White, R. J. Allen, eds. (Space Telescope Science Institute, Baltimore, Md., 1990), pp. 127–131.

Helstrom, C. W.

Krist, J.

J. Krist, The Tiny Tim User’s Manual, V. 4.0 (Space Telescope Science Institute, Baltimore, Md., 1994).

Lanterman, A. D.

O’Sullivan, J. A.

D. L. Snyder, T. J. Schulz, J. A. O’Sullivan, “Deblurring subject to nonnegativity constraints,” IEEE Trans. Signal Process. 40, 1143–1150 (1992).
[Crossref]

Schulz, T. J.

D. L. Snyder, T. J. Schulz, J. A. O’Sullivan, “Deblurring subject to nonnegativity constraints,” IEEE Trans. Signal Process. 40, 1143–1150 (1992).
[Crossref]

Snyder, D. L.

White, R. L.

IEEE Trans. Signal Process. (1)

D. L. Snyder, T. J. Schulz, J. A. O’Sullivan, “Deblurring subject to nonnegativity constraints,” IEEE Trans. Signal Process. 40, 1143–1150 (1992).
[Crossref]

J. Opt. Soc. Am. A (2)

Other (5)

R. L. White, R. J. Allen, eds., Proceedings of Workshop: The Restoration of HST Images and Spectra (Space Telescope Science Institute, Baltimore, Md., 1990).

R. J. Hanish, R. L. White, eds., Proceedings of Workshop: The Restoration of HST Images and Spectra II (Space Telescope Science Institute, Baltimore, Md., 1993).

R. J. Hanisch, “Linear restoration techniques: not all bad,” in Proceedings of Workshop: The Restoration of HST Images and Spectra, R. L. White, R. J. Allen, eds. (Space Telescope Science Institute, Baltimore, Md., 1990), pp. 127–131.

MasPar MP-1 Architecture Specification, MasPar MP-1 System Hardware Manual (MasPar Computer Corporation, Sunnyvale, Calif., 1991), p. 1.2.

J. Krist, The Tiny Tim User’s Manual, V. 4.0 (Space Telescope Science Institute, Baltimore, Md., 1994).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (18)

Fig. 1
Fig. 1

Model of the CCD camera.

Fig. 2
Fig. 2

Computer architecture (from Ref. 7). I/O, input-output.

Fig. 3
Fig. 3

Indexing of the processors.

Fig. 4
Fig. 4

Two-dimensional hierarchical data mapping: D, data element or pixel; L, data layer; solid lines, PE boundaries; dashed lines, boundaries between memory layers on the same PE.

Fig. 5
Fig. 5

Subdivisions and zero padding of the image: darker shading, image to be restored; lighter shading, zero padding; dashed-line area, subimage.

Fig. 6
Fig. 6

Data flow from the image to the PSF during projection from object space to image space. Lower shaded portion, 4 × 4 pixel subimage of the image to be projected; upper shaded portion, 3 × 3 pixel PSF corresponding to the subimage; dashed lines, boundaries of pixels lying in adjacent subimages or PSF’s; arrows, directions of data flow.

Fig. 7
Fig. 7

Data flow from the PSF to the image during projection from object space to image space. Definitions as for Fig. 6.

Fig. 8
Fig. 8

Data flow from the image to the PSF during projection from image space to object space. Definitions as for Fig. 6.

Fig. 9
Fig. 9

Data flow from the PSF to the image during projection from image space to object space. Definitions as for Fig. 6.

Fig. 10
Fig. 10

Four PSF kernels of WF/PC-2 associated with the corner pixels of one of the 800 × 800 pixel CCD chips.

Fig. 11
Fig. 11

Four PSF kernels of WF/PC-1 associated with the corner pixels of one of the 800 × 800 pixel CCD chips. These kernels are shown on the same brightness scale as the kernels in Fig. 10 but are scaled by a factor of 0.5.

Fig. 12
Fig. 12

Simulated star cluster used as the true object λ(i).

Fig. 13
Fig. 13

Simulated data r(j) for WF/PC-1 using a space-variant PSF.

Fig. 14
Fig. 14

Simulated data r(j) for WF/PC-2 using a space-variant PSF.

Fig. 15
Fig. 15

Restoration of simulated data for WF/PC-1 using a space-invariant PSF kernel (top, normal view; bottom, magnified view).

Fig. 16
Fig. 16

Restoration of simulated data for WF/PC-1 using a space-variant PSF kernel (top, normal view; bottom, magnified view).

Fig. 17
Fig. 17

Restoration of simulated data for WF/PC-2 using a space-invariant PSF kernel (top, normal view; bottom, magnified view).

Fig. 18
Fig. 18

Restoration of simulated data for WF/PC-2 using a space-variant PSF kernel (top, normal view; bottom, magnified view).

Tables (4)

Tables Icon

Table 1 Tiny Tim Parameters Used to Simulate PSF Kernels for WF/PC-1

Tables Icon

Table 2 Tiny Tim Parameters Used to Simulate PSF Kernels for WF/PC-2

Tables Icon

Table 3 Computation Times per Iteration of Eq. (3) for the Approximated Space-Invariant PSF Restoration

Tables Icon

Table 4 Computation Times per Iteration of Eq. (3) for the Space-Variant PSF Restoration with PSF Kernel Size N × N and Subimasre Size M × M

Equations (13)

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

r ( j ) = n ( j ) + g ( j )
μ ( j ) = β ( j ) J p ( j | i ) λ ( i ) + μ 0 ( j ) ,
λ ̂ new ( i ) = λ ̂ old ( i ) 1 β ¯ ( i ) J [ β ( j ) p ( j | i ) μ ̂ old ( j ) ] F [ r ( j ) , μ ̂ old ( j ) ] ,
β ¯ ( i ) = J β ( j ) p ( j | i ) ,
μ ̂ old ( j ) = β ( j ) I p ( j | i ) λ ̂ old ( i ) + μ 0 ( j ) ,
F [ r , μ ] = n 0 ( n / n ! ) μ n exp [ ( r n m ) 2 / 2 σ 2 ] n 0 ( 1 / n ! ) μ n exp [ ( r n m ) 2 / 2 σ 2 ] .
r ( j ) = I p ( j | i ) λ ( i ) .
λ ̂ new ( i ) = λ ̂ old ( i ) 1 β ¯ ( i ) J [ p ( j | i ) μ ̂ old ( j ) ] r ( j ) ,
β ¯ ( i ) = J p ( j | i ) ,
μ ̂ old ( j ) = I p ( j | i ) λ ̂ old ( i ) .
y υ r × x υ r = L ny proc × L nx proc
i y proc = y div y υ r , i x proc = x div x υ r , mem = ( x mod x υ r ) + x υ r ( y mod y υ r ) ,
x = ( i x proc × x υ r ) + ( mem mod x υ r ) , y = ( i y proc × y υ r ) + ( mem mod x υ r ) .

Metrics