Abstract

A previously published technique that combined a homomorphic transformation with a locally adaptive algorithm for image restoration in the presence of signal-dependent noise has been adapted for the case when the model for the. signal-dependent noise is unknown. The noise variance required for the homomorphic transformation is estimated from measurements over a small window, and the homomorphic transformation to make the noise additive is incorporated noise into the locally adaptive algorithm, resulting in a modified James–Stein algorithm valid for any signal- dependent noise.

© 1986 Optical Society of America

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References

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  1. H. H. Arsenault, M. Denis, Opt. Lett. 6, 210 (1981).
    [Crossref] [PubMed]
  2. H. H. Arsenault, M. Denis, Can. J. Phys. 61, 309 (1983).
    [Crossref]
  3. G. April, H. H. Arsenault, Opt. Commun. 48, 93 (1983).
    [Crossref]
  4. H. H. Arsenault, M. Levesque, Appl. Opt. 23, 845 (1984).
    [Crossref] [PubMed]
  5. R. Kasturi, J. F. Walkup, T. F. Krile, Appl. Opt. 22, 3537 (1983).
    [Crossref] [PubMed]
  6. J. S. Lee, Comput. Graph. Imag. Proc. 15, 380 (1981).
    [Crossref]
  7. J.-S. Lee, IEEE Trans. Syst. Man Cybern. SMC-13, 85 (1983).
  8. J.-S. Lee, IEEE Trans. Pattern Anal. Mach. Intell. PAMI-2, 165 (1980).
    [Crossref]
  9. D. T. Kuan, A. A. Sawchuk, T. C. Strand, P. Chavel, IEEE Trans. Pattern Anal. Mach. Intell. PAMI-7, 168 (1985).
    [Crossref]
  10. H. H. Arsenault, M. Levesque, “Local statistics image restoration in the absence of a model for signal-dependent noise,” presented at the 13th Congress of the International Commission for Optics, August 20–24, 1984, Sapporo, Tokyo, Japan.

1985 (1)

D. T. Kuan, A. A. Sawchuk, T. C. Strand, P. Chavel, IEEE Trans. Pattern Anal. Mach. Intell. PAMI-7, 168 (1985).
[Crossref]

1984 (1)

1983 (4)

R. Kasturi, J. F. Walkup, T. F. Krile, Appl. Opt. 22, 3537 (1983).
[Crossref] [PubMed]

H. H. Arsenault, M. Denis, Can. J. Phys. 61, 309 (1983).
[Crossref]

G. April, H. H. Arsenault, Opt. Commun. 48, 93 (1983).
[Crossref]

J.-S. Lee, IEEE Trans. Syst. Man Cybern. SMC-13, 85 (1983).

1981 (2)

H. H. Arsenault, M. Denis, Opt. Lett. 6, 210 (1981).
[Crossref] [PubMed]

J. S. Lee, Comput. Graph. Imag. Proc. 15, 380 (1981).
[Crossref]

1980 (1)

J.-S. Lee, IEEE Trans. Pattern Anal. Mach. Intell. PAMI-2, 165 (1980).
[Crossref]

April, G.

G. April, H. H. Arsenault, Opt. Commun. 48, 93 (1983).
[Crossref]

Arsenault, H. H.

H. H. Arsenault, M. Levesque, Appl. Opt. 23, 845 (1984).
[Crossref] [PubMed]

G. April, H. H. Arsenault, Opt. Commun. 48, 93 (1983).
[Crossref]

H. H. Arsenault, M. Denis, Can. J. Phys. 61, 309 (1983).
[Crossref]

H. H. Arsenault, M. Denis, Opt. Lett. 6, 210 (1981).
[Crossref] [PubMed]

H. H. Arsenault, M. Levesque, “Local statistics image restoration in the absence of a model for signal-dependent noise,” presented at the 13th Congress of the International Commission for Optics, August 20–24, 1984, Sapporo, Tokyo, Japan.

Chavel, P.

D. T. Kuan, A. A. Sawchuk, T. C. Strand, P. Chavel, IEEE Trans. Pattern Anal. Mach. Intell. PAMI-7, 168 (1985).
[Crossref]

Denis, M.

H. H. Arsenault, M. Denis, Can. J. Phys. 61, 309 (1983).
[Crossref]

H. H. Arsenault, M. Denis, Opt. Lett. 6, 210 (1981).
[Crossref] [PubMed]

Kasturi, R.

Krile, T. F.

Kuan, D. T.

D. T. Kuan, A. A. Sawchuk, T. C. Strand, P. Chavel, IEEE Trans. Pattern Anal. Mach. Intell. PAMI-7, 168 (1985).
[Crossref]

Lee, J. S.

J. S. Lee, Comput. Graph. Imag. Proc. 15, 380 (1981).
[Crossref]

Lee, J.-S.

J.-S. Lee, IEEE Trans. Syst. Man Cybern. SMC-13, 85 (1983).

J.-S. Lee, IEEE Trans. Pattern Anal. Mach. Intell. PAMI-2, 165 (1980).
[Crossref]

Levesque, M.

H. H. Arsenault, M. Levesque, Appl. Opt. 23, 845 (1984).
[Crossref] [PubMed]

H. H. Arsenault, M. Levesque, “Local statistics image restoration in the absence of a model for signal-dependent noise,” presented at the 13th Congress of the International Commission for Optics, August 20–24, 1984, Sapporo, Tokyo, Japan.

Sawchuk, A. A.

D. T. Kuan, A. A. Sawchuk, T. C. Strand, P. Chavel, IEEE Trans. Pattern Anal. Mach. Intell. PAMI-7, 168 (1985).
[Crossref]

Strand, T. C.

D. T. Kuan, A. A. Sawchuk, T. C. Strand, P. Chavel, IEEE Trans. Pattern Anal. Mach. Intell. PAMI-7, 168 (1985).
[Crossref]

Walkup, J. F.

Appl. Opt. (2)

Can. J. Phys. (1)

H. H. Arsenault, M. Denis, Can. J. Phys. 61, 309 (1983).
[Crossref]

Comput. Graph. Imag. Proc. (1)

J. S. Lee, Comput. Graph. Imag. Proc. 15, 380 (1981).
[Crossref]

IEEE Trans. Pattern Anal. Mach. Intell. (2)

J.-S. Lee, IEEE Trans. Pattern Anal. Mach. Intell. PAMI-2, 165 (1980).
[Crossref]

D. T. Kuan, A. A. Sawchuk, T. C. Strand, P. Chavel, IEEE Trans. Pattern Anal. Mach. Intell. PAMI-7, 168 (1985).
[Crossref]

IEEE Trans. Syst. Man Cybern. (1)

J.-S. Lee, IEEE Trans. Syst. Man Cybern. SMC-13, 85 (1983).

Opt. Commun. (1)

G. April, H. H. Arsenault, Opt. Commun. 48, 93 (1983).
[Crossref]

Opt. Lett. (1)

Other (1)

H. H. Arsenault, M. Levesque, “Local statistics image restoration in the absence of a model for signal-dependent noise,” presented at the 13th Congress of the International Commission for Optics, August 20–24, 1984, Sapporo, Tokyo, Japan.

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Figures (4)

Fig. 1
Fig. 1

Original undegraded image.

Fig. 2
Fig. 2

Image degraded by the noise given by Eq. (6)

Fig. 3
Fig. 3

Restored image when the model of the noise is assumed to be unknown.

Fig. 4
Fig. 4

Restored image using a noise matrix smoothed with the function of expression (5).

Tables (1)

Tables Icon

Table 1 MSE Reduction in Restored Images

Equations (6)

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g ( s ) = K d s / σ s ( s ) ,
g i j = s i j / σ i j ,
S ^ i j = r ¯ i j + ( 1 - σ n 2 / V i j ) ( r i j - r ¯ i j ) ,
S i j = r i j + ( 1 - 1 / V i j ) ( r i j - r ¯ i j ) .
[ 1 / 16 1 / 8 1 / 16 1 / 8 1 / 4 1 / 8 1 / 16 1 / 8 1 / 16 ] .
R = S + 15 n + 4 S n + 0.4 S n ,

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