Abstract

An algorithm is described which reduces speckle noise in images. It is a nonlinear algorithm based on geometric concepts. Tests were performed on synthetic aperture radar images which show that it compares favorably with a 3 × 3 median filter.

© 1985 Optical Society of America

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References

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  1. J. W. Tukey, “Nonlinear (Nonsuperposable) Methods for Smoothing Data,” in Congressional Record 1974, EASCON, p. 673.
  2. J. W. Tukey, Exploratory Data Analysis (Addison-Wesley, Reading, Mass., 1977).
  3. T. S. Huang, G. J. Yang, G. Y. Yang, “A Fast Two-Dimensional Medium Filtering Algorithm,” IEEE Trans. Acoust. Speech Signal Process. ASSP-27, 13 (1979).
    [CrossRef]
  4. T. S. Huang, G. J. Yang, “Median Filters and Their Applications to Image Processing,” School of Electrical Engineering, Purdue U., West Lafayette, Ind., TR. EE 80-1 (Jan.1980).
  5. S. G. Tyan, “Median Filtering: Deterministic Properties,” in Two-Dimensional Digital Signal Processing. Vol. 2: Transforms and Median Filters, T. S. Huang, Ed. (Springer, Berlin, 1981).
    [CrossRef]
  6. N. C. Gallagher, G. L. Wise, “A Theoretical Analysis of the Properties of Median Filters,” IEEE Trans. Acoust. Speech Signal Process. ASSP-29, 1136 (1981).
    [CrossRef]
  7. T. A. Nodes, N. C. Gallagher, “Median Filters: Some Modifications and Their Properties,” IEEE Trans. Acoust. Speech Signal Process. ASSP-30, 739 (1982).
    [CrossRef]
  8. G. R. Arce, N. C. Gallagher, “State Description for the Root-Signal Set of Median Filters,” IEEE Trans. Acoust. Speech Signal Process. ASSP-30, 894 (1982).
    [CrossRef]
  9. J. W. Goodman, “Statistical Properties of Laser Speckle Patterns,” in Laser Speckle and Related Phenomena, J. C. Dainty, Ed. (Springer, Berlin, 1975), pp. 9–75.
    [CrossRef]

1982 (2)

T. A. Nodes, N. C. Gallagher, “Median Filters: Some Modifications and Their Properties,” IEEE Trans. Acoust. Speech Signal Process. ASSP-30, 739 (1982).
[CrossRef]

G. R. Arce, N. C. Gallagher, “State Description for the Root-Signal Set of Median Filters,” IEEE Trans. Acoust. Speech Signal Process. ASSP-30, 894 (1982).
[CrossRef]

1981 (1)

N. C. Gallagher, G. L. Wise, “A Theoretical Analysis of the Properties of Median Filters,” IEEE Trans. Acoust. Speech Signal Process. ASSP-29, 1136 (1981).
[CrossRef]

1979 (1)

T. S. Huang, G. J. Yang, G. Y. Yang, “A Fast Two-Dimensional Medium Filtering Algorithm,” IEEE Trans. Acoust. Speech Signal Process. ASSP-27, 13 (1979).
[CrossRef]

Arce, G. R.

G. R. Arce, N. C. Gallagher, “State Description for the Root-Signal Set of Median Filters,” IEEE Trans. Acoust. Speech Signal Process. ASSP-30, 894 (1982).
[CrossRef]

Gallagher, N. C.

G. R. Arce, N. C. Gallagher, “State Description for the Root-Signal Set of Median Filters,” IEEE Trans. Acoust. Speech Signal Process. ASSP-30, 894 (1982).
[CrossRef]

T. A. Nodes, N. C. Gallagher, “Median Filters: Some Modifications and Their Properties,” IEEE Trans. Acoust. Speech Signal Process. ASSP-30, 739 (1982).
[CrossRef]

N. C. Gallagher, G. L. Wise, “A Theoretical Analysis of the Properties of Median Filters,” IEEE Trans. Acoust. Speech Signal Process. ASSP-29, 1136 (1981).
[CrossRef]

Goodman, J. W.

J. W. Goodman, “Statistical Properties of Laser Speckle Patterns,” in Laser Speckle and Related Phenomena, J. C. Dainty, Ed. (Springer, Berlin, 1975), pp. 9–75.
[CrossRef]

Huang, T. S.

T. S. Huang, G. J. Yang, G. Y. Yang, “A Fast Two-Dimensional Medium Filtering Algorithm,” IEEE Trans. Acoust. Speech Signal Process. ASSP-27, 13 (1979).
[CrossRef]

T. S. Huang, G. J. Yang, “Median Filters and Their Applications to Image Processing,” School of Electrical Engineering, Purdue U., West Lafayette, Ind., TR. EE 80-1 (Jan.1980).

Nodes, T. A.

T. A. Nodes, N. C. Gallagher, “Median Filters: Some Modifications and Their Properties,” IEEE Trans. Acoust. Speech Signal Process. ASSP-30, 739 (1982).
[CrossRef]

Tukey, J. W.

J. W. Tukey, Exploratory Data Analysis (Addison-Wesley, Reading, Mass., 1977).

J. W. Tukey, “Nonlinear (Nonsuperposable) Methods for Smoothing Data,” in Congressional Record 1974, EASCON, p. 673.

Tyan, S. G.

S. G. Tyan, “Median Filtering: Deterministic Properties,” in Two-Dimensional Digital Signal Processing. Vol. 2: Transforms and Median Filters, T. S. Huang, Ed. (Springer, Berlin, 1981).
[CrossRef]

Wise, G. L.

N. C. Gallagher, G. L. Wise, “A Theoretical Analysis of the Properties of Median Filters,” IEEE Trans. Acoust. Speech Signal Process. ASSP-29, 1136 (1981).
[CrossRef]

Yang, G. J.

T. S. Huang, G. J. Yang, G. Y. Yang, “A Fast Two-Dimensional Medium Filtering Algorithm,” IEEE Trans. Acoust. Speech Signal Process. ASSP-27, 13 (1979).
[CrossRef]

T. S. Huang, G. J. Yang, “Median Filters and Their Applications to Image Processing,” School of Electrical Engineering, Purdue U., West Lafayette, Ind., TR. EE 80-1 (Jan.1980).

Yang, G. Y.

T. S. Huang, G. J. Yang, G. Y. Yang, “A Fast Two-Dimensional Medium Filtering Algorithm,” IEEE Trans. Acoust. Speech Signal Process. ASSP-27, 13 (1979).
[CrossRef]

IEEE Trans. Acoust. Speech Signal Process. (4)

T. S. Huang, G. J. Yang, G. Y. Yang, “A Fast Two-Dimensional Medium Filtering Algorithm,” IEEE Trans. Acoust. Speech Signal Process. ASSP-27, 13 (1979).
[CrossRef]

N. C. Gallagher, G. L. Wise, “A Theoretical Analysis of the Properties of Median Filters,” IEEE Trans. Acoust. Speech Signal Process. ASSP-29, 1136 (1981).
[CrossRef]

T. A. Nodes, N. C. Gallagher, “Median Filters: Some Modifications and Their Properties,” IEEE Trans. Acoust. Speech Signal Process. ASSP-30, 739 (1982).
[CrossRef]

G. R. Arce, N. C. Gallagher, “State Description for the Root-Signal Set of Median Filters,” IEEE Trans. Acoust. Speech Signal Process. ASSP-30, 894 (1982).
[CrossRef]

Other (5)

J. W. Goodman, “Statistical Properties of Laser Speckle Patterns,” in Laser Speckle and Related Phenomena, J. C. Dainty, Ed. (Springer, Berlin, 1975), pp. 9–75.
[CrossRef]

T. S. Huang, G. J. Yang, “Median Filters and Their Applications to Image Processing,” School of Electrical Engineering, Purdue U., West Lafayette, Ind., TR. EE 80-1 (Jan.1980).

S. G. Tyan, “Median Filtering: Deterministic Properties,” in Two-Dimensional Digital Signal Processing. Vol. 2: Transforms and Median Filters, T. S. Huang, Ed. (Springer, Berlin, 1981).
[CrossRef]

J. W. Tukey, “Nonlinear (Nonsuperposable) Methods for Smoothing Data,” in Congressional Record 1974, EASCON, p. 673.

J. W. Tukey, Exploratory Data Analysis (Addison-Wesley, Reading, Mass., 1977).

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Figures (10)

Fig. 1
Fig. 1

Radar image of Willow Run Airport. The boxed section appears in Fig. 2(a).

Fig. 2
Fig. 2

(a) Original image. (b) Four iterations of geometric filter. (c) Ten iterations of geometric filter. (d) Period 2 median root of original image.

Fig. 3
Fig. 3

(a) Shaded and shadowed version of original image. (b) Shaded and shadowed version of ten iterations of geometric filter. (c) Shaded and shadowed version of period 2 median root of original image.

Fig. 4
Fig. 4

Patterns used by the 8-hull algorithm.

Fig. 5
Fig. 5

(a) Original set. (b) One iteration of 8-hull algorithm. (c) Two iterations. (d) Three iterations. This is invariant under further iterations.

Fig. 6
Fig. 6

Allowable 90° turns in the boundary. These are exceptions to the rule.

Fig. 7
Fig. 7

(a) Original set. (b) One iteration of complementary hulling algorithm. (c) Two iterations. (d) Three iterations. (e) Nine iterations. This is invariant under further iterations.

Fig. 8
Fig. 8

(a) Original set. (b) One iteration of complementary hulling algorithm. (c) Two iterations. (d) Fourteen iterations. (e) Fifteen iterations. This is invariant under further iterations.

Fig. 9
Fig. 9

(a) Original set. (b) One iteration of complementary hulling algorithm. (c) Two iterations. (d) Three iterations. This is invariant under further iterations.

Fig. 10
Fig. 10

(a) Curve. (b) Umbra of curve. (c) Complement of umbra.

Tables (3)

Tables Icon

Table I Speckle Indices

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Table II Reduction Rates for Square Towers

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Table III Reduction Rates for Walls

Equations (3)

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σ ( m , n ) = max p ( m + i , n + j ) min p ( m + i , n + j ) . 1 i 1 1 i 1 1 j 1 1 j 1
μ ( m , n ) = 1 9 i , j = 1 1 p ( m + i , n + j ) .
1 ( N 2 ) 2 m , n = 2 N 1 σ ( m , n ) μ ( m , n ) .

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