Abstract

A variation of matched filtering using 1-D code sequences with near optimum correlation properties is applied to the reconstruction of coded-source or coded-scan tomographic imagery. The reconstructed image enjoys a higher SNR than imagery reconstructed with conventional matched filtering. A major advantage of using code sequences is the elimination of noise and secondary images that result from the sidelobes of the autocorrelation function of nonnegative functions or sequences.

© 1978 Optical Society of America

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References

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  1. C. Brown, J. Appl. Phys. 45, 1806 (1974).
    [CrossRef]
  2. J. K. Wolf, U. Mass.; private communication (25November1977).
  3. D. Calabro, J. K. Wolf, Inf. Control 11, 537 (1962).
    [CrossRef]
  4. F. Mandelkorn, H. Stark, Appl. Opt. 15, 1881 (1976).
    [CrossRef] [PubMed]
  5. F. Mandelkorn, H. Stark, Appl. Opt. 17, 175 (1978).
    [CrossRef] [PubMed]

1978 (1)

1976 (1)

1974 (1)

C. Brown, J. Appl. Phys. 45, 1806 (1974).
[CrossRef]

1962 (1)

D. Calabro, J. K. Wolf, Inf. Control 11, 537 (1962).
[CrossRef]

Brown, C.

C. Brown, J. Appl. Phys. 45, 1806 (1974).
[CrossRef]

Calabro, D.

D. Calabro, J. K. Wolf, Inf. Control 11, 537 (1962).
[CrossRef]

Mandelkorn, F.

Stark, H.

Wolf, J. K.

D. Calabro, J. K. Wolf, Inf. Control 11, 537 (1962).
[CrossRef]

J. K. Wolf, U. Mass.; private communication (25November1977).

Appl. Opt. (2)

Inf. Control (1)

D. Calabro, J. K. Wolf, Inf. Control 11, 537 (1962).
[CrossRef]

J. Appl. Phys. (1)

C. Brown, J. Appl. Phys. 45, 1806 (1974).
[CrossRef]

Other (1)

J. K. Wolf, U. Mass.; private communication (25November1977).

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Figures (6)

Fig. 1
Fig. 1

Geometry considered for tomographic image reconstruction by correlation with near-perfect sequences.

Fig. 2
Fig. 2

Top view of the computer-realized phantom.

Fig. 3
Fig. 3

The multiply exposed image resulting from the source-coding sequence [1,0,0,1,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0].

Fig. 4
Fig. 4

Reconstruction of the number 6 by cross-correlating the sequence cited in Fig. 3 with the postprocessing sequence [1,−1,−1,1,−1,1,1,1,−1,−1,1,−1,1,1,1,−1,−1,1,−1].

Fig. 5
Fig. 5

Reconstruction of the number 12 by the technique cited in Fig. 4. The scaling parameters are different in the two figures.

Fig. 6
Fig. 6

Zoom view of the reconstructed 12 showing the structure of the unwanted artifacts in the image field.

Equations (23)

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R ( k ) = l a l a l + k .
R ( k ) = { 4 , k = 0 , ± 4 , ± 8 , etc . , 0 , k = ± 1 , ± 2 , ± 3 , ± 4 , ± 5 , etc .
R ( k ) = { 7 , k = 0 , ± 7 , ± 14 , etc . , 1 , k = ± 1 , ± 2 , ± 3 , ± 4 , ± 5 , ± 6 , etc .
Γ ( k ) = l = 1 N a l b l + k = { N + 1 2 , k = 0 , ± N , ± 2 N , etc . , 0 , otherwise .
{ 1,1,1,1 , 1,1 , 1,1,1 , 1 , 1,1 , 1 , 1 , 1 }
{ 1,1,1,1,0,1,0,1,1,0,0,1,0,0,0 } ,
Γ ( k ) = l = 1 15 a l b l + k = { 8 , k = 0 , ± 15 , ± 30 , , 0 , elsewhere .
q = 5 , p = 3 q = 7 , p = 5 q = 13 , p = 11
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1. ( basic pattern )
0 0 0 1 1 0 1 0 1 1 0 1 1 1 0 ( basic pattern ) ,
t ( r ) = j = 1 K P j ( r M j ) * h ( r M h j ) ,
t ( r ) = j = 1 K P j * h j ,
[ j = 1 K P j * h j ] g i
= j = 1 K P j * Γ i j
P ˆ i + noise ,
Γ i j ( r ) = 0 for all i j and all r
Γ i i ( r ) = { A , r = 0 , 0 , r 0.
{ a l } = { 1,1 , 1 , 1,1 , 1,1 }
{ b l } = { 1,1,0,0,1,0,1 }
Γ ( k ) = l = 1 7 a l b l + k = { 4 , k = 0 , ± 7 , ± 14 , etc . 0 , otherwise .
{ 1,0,0,1,0,1 , 1,1,0,0,1,0,1 basic period , 1,1,0,0,1,0 }
Γ ( k ) = { 4 , k = 0 0 , k = ± 1 , ± 2 , ± 3 , ± 4 , ± 5 , ± 6.
2 Δ = d 1 + d 2 d 1 ( d 1 + z ) z x .

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