Abstract

A bandwidth-compression scheme for two-dimensional data is presented that incorporates the Radon transform. There are three advantages to this approach: only one-dimensional operations are required, the dynamic range requirements of the compression are reduced by a filtering step associated with the inverse Radon transform, and the technique is readily adaptive to the data structure. A rectilinear object is compressed to demonstrate the algorithm.

© 1983 Optical Society of America

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References

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  1. J. Radon, “Über die Bestimmung von Funktionen durch ihre Integralwerte längs gewisser Mannigfaltigkeiten,” Ber. Saechs. Akad. Wiss. (Leipzig) 69, 262–278 (1917).
  2. H. H. Barrett, W. Swindell, Radiological Imaging: Theory of Image Formation, Detection, and Processing (Academic, New York, 1981), Vols. I and II.
  3. H. H. Barrett, “The Radon transform and its applications,” in Progress in Optics, E. Wolf, ed. (to be published).
  4. H. H. Barrett, “Optical processing in Radon space,” Opt. Lett. 7, 248–250, (1982).
    [CrossRef] [PubMed]
  5. G. Eichmann, P. Z. Dong, “Coherent optical production of the Hough transform,” presented at the Conference on Optics, Los Alamos, New Mexico, April 11–15, 1983.
  6. W. G. Wee, “Application of projection techniques to image transmission,” presented at the Techniques of Three-Dimensional Reconstruction International Workshop, Upton, New York, July 16–19, 1974.
  7. W. K. Pratt, Digital Image Processing (Wiley, New York, 1978).

1982 (1)

1917 (1)

J. Radon, “Über die Bestimmung von Funktionen durch ihre Integralwerte längs gewisser Mannigfaltigkeiten,” Ber. Saechs. Akad. Wiss. (Leipzig) 69, 262–278 (1917).

Barrett, H. H.

H. H. Barrett, “Optical processing in Radon space,” Opt. Lett. 7, 248–250, (1982).
[CrossRef] [PubMed]

H. H. Barrett, W. Swindell, Radiological Imaging: Theory of Image Formation, Detection, and Processing (Academic, New York, 1981), Vols. I and II.

H. H. Barrett, “The Radon transform and its applications,” in Progress in Optics, E. Wolf, ed. (to be published).

Dong, P. Z.

G. Eichmann, P. Z. Dong, “Coherent optical production of the Hough transform,” presented at the Conference on Optics, Los Alamos, New Mexico, April 11–15, 1983.

Eichmann, G.

G. Eichmann, P. Z. Dong, “Coherent optical production of the Hough transform,” presented at the Conference on Optics, Los Alamos, New Mexico, April 11–15, 1983.

Pratt, W. K.

W. K. Pratt, Digital Image Processing (Wiley, New York, 1978).

Radon, J.

J. Radon, “Über die Bestimmung von Funktionen durch ihre Integralwerte längs gewisser Mannigfaltigkeiten,” Ber. Saechs. Akad. Wiss. (Leipzig) 69, 262–278 (1917).

Swindell, W.

H. H. Barrett, W. Swindell, Radiological Imaging: Theory of Image Formation, Detection, and Processing (Academic, New York, 1981), Vols. I and II.

Wee, W. G.

W. G. Wee, “Application of projection techniques to image transmission,” presented at the Techniques of Three-Dimensional Reconstruction International Workshop, Upton, New York, July 16–19, 1974.

Ber. Saechs. Akad. Wiss. (Leipzig) (1)

J. Radon, “Über die Bestimmung von Funktionen durch ihre Integralwerte längs gewisser Mannigfaltigkeiten,” Ber. Saechs. Akad. Wiss. (Leipzig) 69, 262–278 (1917).

Opt. Lett. (1)

Other (5)

G. Eichmann, P. Z. Dong, “Coherent optical production of the Hough transform,” presented at the Conference on Optics, Los Alamos, New Mexico, April 11–15, 1983.

W. G. Wee, “Application of projection techniques to image transmission,” presented at the Techniques of Three-Dimensional Reconstruction International Workshop, Upton, New York, July 16–19, 1974.

W. K. Pratt, Digital Image Processing (Wiley, New York, 1978).

H. H. Barrett, W. Swindell, Radiological Imaging: Theory of Image Formation, Detection, and Processing (Academic, New York, 1981), Vols. I and II.

H. H. Barrett, “The Radon transform and its applications,” in Progress in Optics, E. Wolf, ed. (to be published).

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Figures (2)

Fig. 1
Fig. 1

(a) Reconstruction from Radon projections without thresholding and nominal 8-bit quantization (8 bits/pixel), (b) truncation of 48% of components with 3-bit quantization (1.6 bits/pixel), (c) truncation of 66% of components with 3-bit quantization (1.1 bits/pixel), (d) truncation of 48% of components with two-bit quantization (1.1 bits/pixel).

Fig. 2
Fig. 2

Truncated and quantized Fourier components of Fig. 1(d).

Equations (5)

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λ ϕ ( p ) = f ( r ) δ ( p r · n ) d 2 r ,
Λ ϕ ( ν ) = f ( r ) exp ( 2 π i ν r · n ) d 2 r = F ( ρ ) | ρ = ν n ,
f ( r ) = 0 π d ϕ [ d ν { | ν | Λ ϕ ( ν ) } exp ( 2 π i ν p ) ] p = n · r .
0 C ϕ | | ν | Λ ϕ ( ν ) | d ν = S ϕ ( S ϕ S ϕ max ) T ,
S ϕ 0 | | ν | Λ ϕ ( ν ) | d ν ,

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